Question

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).

Answer 1

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:

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

Answer: correct choice is A.