Question

use the long division method to find the result when $9x^3 + 21x^2 + 16x + 10$ is divided by $3x + 5$.

Explanation:

Step1: Divide leading terms

$\frac{9x^3}{3x} = 3x^2$
Multiply divisor by $3x^2$: $3x^2(3x+5)=9x^3+15x^2$
Subtract from dividend:
$(9x^3+21x^2+16x+10)-(9x^3+15x^2)=6x^2+16x+10$

Step2: Divide new leading terms

$\frac{6x^2}{3x} = 2x$
Multiply divisor by $2x$: $2x(3x+5)=6x^2+10x$
Subtract from current polynomial:
$(6x^2+16x+10)-(6x^2+10x)=6x+10$

Step3: Divide final leading terms

$\frac{6x}{3x} = 2$
Multiply divisor by $2$: $2(3x+5)=6x+10$
Subtract from current polynomial:
$(6x+10)-(6x+10)=0$

Answer:

$3x^2 + 2x + 2$