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Katarina [22]
3 years ago
13

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).

Mathematics
1 answer:
daser333 [38]3 years ago
8 0

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

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

Here x+8 is quotient and -4x+31 is remainder.

2 step: Substitute previous result into the fraction:

\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}.

Answer: correct choice is A.

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