Question

question
use the long division method to find the result when $2x^3 - 13x^2 + 20x - 4$ is divided by $x - 2$.

Explanation:

Step1: Divide leading terms

$\frac{2x^3}{x} = 2x^2$
Multiply $x-2$ by $2x^2$: $2x^2(x-2)=2x^3-4x^2$
Subtract from dividend:
$(2x^3-13x^2+20x-4)-(2x^3-4x^2) = -9x^2+20x-4$

Step2: Divide new leading terms

$\frac{-9x^2}{x} = -9x$
Multiply $x-2$ by $-9x$: $-9x(x-2)=-9x^2+18x$
Subtract:
$(-9x^2+20x-4)-(-9x^2+18x) = 2x-4$

Step3: Divide final leading terms

$\frac{2x}{x} = 2$
Multiply $x-2$ by $2$: $2(x-2)=2x-4$
Subtract:
$(2x-4)-(2x-4) = 0$

Answer:

$2x^2 - 9x + 2$