Question

1. ((x^5 - 9x^2 - 1) div (x - 2))

Explanation:

Step1: Set up polynomial long division

Divide $x^3 - 9x^2 + 0x - 1$ by $x-2$ (add $0x$ for missing term)

Step2: Divide leading terms

$\frac{x^3}{x} = x^2$, multiply divisor: $x^2(x-2)=x^3-2x^2$
Subtract: $(x^3-9x^2)-(x^3-2x^2)=-7x^2$
Bring down $0x$: $-7x^2 + 0x$

Step3: Divide leading terms again

$\frac{-7x^2}{x} = -7x$, multiply divisor: $-7x(x-2)=-7x^2+14x$
Subtract: $(-7x^2+0x)-(-7x^2+14x)=-14x$
Bring down $-1$: $-14x - 1$

Step4: Divide leading terms a third time

$\frac{-14x}{x} = -14$, multiply divisor: $-14(x-2)=-14x+28$
Subtract: $(-14x-1)-(-14x+28)=-29$

Answer:

Quotient: $x^2 - 7x - 14$, Remainder: $-29$, or written as $x^2 - 7x - 14 + \frac{-29}{x-2}$