Question

1. $(x^{3}-4x^{2}-8x - 6)div(x - 5)$

Explanation:

Step1: Set up polynomial long division

Divide $x^3-4x^2-8x-6$ by $x-5$

Step2: 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:
$(x^3-4x^2-8x-6)-(x^3-5x^2)=x^2-8x-6$

Step3: Divide new leading terms

$\frac{x^2}{x}=x$, multiply divisor by $x$:
$x(x-5)=x^2-5x$
Subtract from current remainder:
$(x^2-8x-6)-(x^2-5x)=-3x-6$

Step4: Divide new leading terms

$\frac{-3x}{x}=-3$, multiply divisor by $-3$:
$-3(x-5)=-3x+15$
Subtract from current remainder:
$(-3x-6)-(-3x+15)=-21$

Answer:

Quotient: $x^2+x-3$, Remainder: $-21$, or written as $x^2+x-3+\frac{-21}{x-5}$