Question

question
use the long division method to find the result when $9x^3 + 9x^2 + 5x + 2$ is divided by $3x + 2$.

Explanation:

Step1: Divide leading terms

$\frac{9x^3}{3x} = 3x^2$
Multiply divisor by $3x^2$: $3x^2(3x+2)=9x^3+6x^2$
Subtract from dividend:
$(9x^3+9x^2+5x+2)-(9x^3+6x^2)=3x^2+5x+2$

Step2: Divide new leading terms

$\frac{3x^2}{3x} = x$
Multiply divisor by $x$: $x(3x+2)=3x^2+2x$
Subtract from current polynomial:
$(3x^2+5x+2)-(3x^2+2x)=3x+2$

Step3: Divide final leading terms

$\frac{3x}{3x} = 1$
Multiply divisor by $1$: $1(3x+2)=3x+2$
Subtract from current polynomial:
$(3x+2)-(3x+2)=0$

Answer:

$3x^2 + x + 1$