Question

use the long division method to find the result when $3x^{3}+20x^{2}+20x - 25$ is divided by $x + 5$.

Explanation:

Step1: Divide leading terms

$\frac{3x^3}{x} = 3x^2$
Multiply divisor by $3x^2$: $3x^2(x+5)=3x^3+15x^2$
Subtract from dividend:
$(3x^3+20x^2+20x-25)-(3x^3+15x^2)=5x^2+20x-25$

Step2: Divide new leading terms

$\frac{5x^2}{x}=5x$
Multiply divisor by $5x$: $5x(x+5)=5x^2+25x$
Subtract:
$(5x^2+20x-25)-(5x^2+25x)=-5x-25$

Step3: Divide new leading terms

$\frac{-5x}{x}=-5$
Multiply divisor by $-5$: $-5(x+5)=-5x-25$
Subtract:
$(-5x-25)-(-5x-25)=0$

Answer:

$3x^2 + 5x - 5$