Question

question
use the long division method to find the result when $x^3 - 7x^2 + 5x + 25$ is divided by $x - 5$.

Explanation:

Step1: Divide leading terms

$\frac{x^3}{x} = x^2$
Multiply divisor by $x^2$: $x^2(x-5) = x^3 - 5x^2$
Subtract from dividend:
$(x^3 - 7x^2 + 5x + 25) - (x^3 - 5x^2) = -2x^2 + 5x$

Step2: Divide new leading terms

$\frac{-2x^2}{x} = -2x$
Multiply divisor by $-2x$: $-2x(x-5) = -2x^2 + 10x$
Subtract from current remainder:
$(-2x^2 + 5x) - (-2x^2 + 10x) = -5x + 25$

Step3: Divide new leading terms

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

Answer:

$x^2 - 2x - 5$