kayley9963
kayley9963 kayley9963
  • 13-09-2018
  • Mathematics
contestada

Select the correct answer. Rewrite the expression x^3+10x^2+13x+39/x^2+2x+1 in the form q(x)+r(x)/b(x).

Select the correct answer Rewrite the expression x310x213x39x22x1 in the form qxrxbx class=

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frika
frika frika
  • 13-09-2018

1 step: Divide the polynomial [tex]x^3+10x^2+13x+39[/tex] by the polynomial [tex]x^2+2x+1[/tex] with remainder:

[tex]x^3+10x^2+13x+39=(x^2+2x+1)(x+8)+(-4x+31).[/tex]

Here [tex]x+8[/tex] is quotient and [tex]-4x+31[/tex] is remainder.

2 step: Substitute previous result into the fraction:

[tex]\dfrac{x^3+10x^2+13x+39}{x^2+2x+1}=\dfrac{(x^2+2x+1)(x+8)+(-4x+31)}{x^2+2x+1}=\\ \\=\dfrac{(x^2+2x+1)(x+8)}{x^2+2x+1}+\dfrac{-4x+31}{x^2+2x+1}=(x+8)+\dfrac{-4x+31}{x^2+2x+1}.[/tex]

Answer: correct choice is A.

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