exam1.mw

• 1. Consider the polynomial Typesetting:-mrow(Typesetting:-mi("p"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("3"), superscriptshift = "0"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("3"), Typesetting:-mo("⋅", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2"), superscriptshift = "0"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("8."), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"))Give Maple commands (with output)
  • (a) to show that p is irreducible over the rational numbers :
  • (b) to factor p symbolically into a product of linear polynomials, adding sufficiently many formal roots :
  • (c) to factor p numerically :
  • (d) to show the relation between the numerical and the symbolic factorization :
• 2. Execute the commands Typesetting:-mrow(Typesetting:-mi(""))
  • (a) Explain why the third command does not give the desired result.
  • (b) Modify ONLY the third command so that is returnsTypesetting:-mrow(Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msub(Typesetting:-mi("x"), Typesetting:-mn("1"), subscriptshift = "0", placeholder = "false"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msub(Typesetting:-mi("x"), Typesetting:-mn("2"), subscriptshift = "0", placeholder = "false"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msub(Typesetting:-mi("x"), Typesetting:-mn("3"), subscriptshift = "0", placeholder = "false"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msub(Typesetting:-mi("x"), Typesetting:-mn("4"), subscriptshift = "0", placeholder = "false"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msub(Typesetting:-mi("x"), Typesetting:-mn("5"), subscriptshift = "0", placeholder = "false"), Typesetting:-mo(".", form = "infix", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"))
• 3. The sequence Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mfrac(Typesetting:-mn("7"), Typesetting:-mn("5"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo(",", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mfrac(Typesetting:-mn("141"), Typesetting:-mn("100"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo(",", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mfrac(Typesetting:-mn("707"), Typesetting:-mn("500"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo(",", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mfrac(Typesetting:-mn("7071"), Typesetting:-mn("5000"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo(",", form = "infix", fence = "false", separator = "true", lspace = "0em", rspace = "verythickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mfrac(Typesetting:-mn("66441"), Typesetting:-mn("46981"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"))
  • (a) How many decimal places in Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mfrac(Typesetting:-mn("66441"), Typesetting:-mn("46981"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mi("")) as rational approximation for Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-msqrt(Typesetting:-mn("2"), foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mi("")) are correct?
  • (b) What is the next element in the sequence?
  • [Untitled Section]
  • [Untitled Section]
  • [Untitled Section]
• 4. Do q := (x/y - 1)/(y/x - 1); and consider the expression assigned to q.
  • (a) Give the Maple command(s) to display the internal representation of this expression.
  • (b) Draw the directed acyclic graph which represents this expression.
  • (c) Explain the outcome of subs(-1=+2,q). Why are all the divisions gone?
• 5. Let Typesetting:-mrow(Typesetting:-mi("r"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("14"), superscriptshift = "0"), Typesetting:-mo("−", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("8"), Typesetting:-mo("⋅", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("12"), superscriptshift = "0"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("9"), Typesetting:-mo("⋅", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mi("x"))), Typesetting:-mi("")), Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("13"), superscriptshift = "0"), Typesetting:-mo("+", form = "infix", fence = "false", separator = "false", lspace = "mediummathspace", rspace = "mediummathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("14"), Typesetting:-mo("⋅", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("7"), superscriptshift = "0"), Typesetting:-mo("−", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("3"), Typesetting:-mo("⋅", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("5"), superscriptshift = "0"), Typesetting:-mi(""))), Typesetting:-mi("")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mi("")) . Give all Maple commands and their output when answering the questions below.
  • (a) Convert Typesetting:-mrow(Typesetting:-mi("r"), Typesetting:-mo("⁢", form = "", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"))into a Horner form.
  • (b) Compare to the given form of Typesetting:-mrow(Typesetting:-mi("r")), how many arithmetical operations are gained when using the Horner form of Typesetting:-mrow(Typesetting:-mi("r"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "verythinmathspace", rspace = "verythinmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"))to evaluate Typesetting:-mrow(Typesetting:-mi("r"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "verythinmathspace", rspace = "verythinmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("?", form = "infix", fence = "false", separator = "false", lspace = "verythinmathspace", rspace = "verythinmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 2", size = "16", foreground = "[0,0,0]", background = "[255,255,255]"))
  • (c) What is the most efficient way to evaluate Typesetting:-mrow(Typesetting:-mi("r")) ?
• 6. Consider the polynomials Typesetting:-mrow(Typesetting:-mi("p"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2"), superscriptshift = "0"), Typesetting:-mo("−", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mfrac(Typesetting:-mn("7"), Typesetting:-mn("4"), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mi("")) and Typesetting:-mrow(Typesetting:-mi("q"), Typesetting:-mo("⁢", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2"), superscriptshift = "0"), Typesetting:-mo("−", form = "", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mo("⁢", form = "", fence = "false", separator = "false", lspace = "0em", rspace = "0em", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "Heading 1", size = "18", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("1.75."))
  • (a) Are these polynomials the same or are they different?
  • (b) Explain why the outcome of factor is then so different.