Use synthetic division to find the quotient and remainder when $\newline$ $-x+4x^{2}-8$ is divided by $\newline$ $x-2$ by completing the parts below. $\newline$ (a) Complete this synthetic division table. $\newline$ (b) Write your answer in the following form: Quotient $\newline$ $+\left(\text{＂ Remainder ＂}\right)/(x-2)$ . $\newline$ $(-x^{3}+4x^{2}-8)/(x-2)=\square+(\square)/(x-2)$ $\newline$ Continue

Full solution

Q. Use synthetic division to find the quotient and remainder when

\newline

-x+4x^{2}-8

is divided by

\newline

x-2

by completing the parts below.

\newline

(a) Complete this synthetic division table.

\newline

(b) Write your answer in the following form: Quotient

\newline

+\left(\text{＂ Remainder ＂}\right)/(x-2)

\newline

(-x^{3}+4x^{2}-8)/(x-2)=\square+(\square)/(x-2)

\newline

Continue

Identify Coefficients: Identify the coefficients of the polynomial for synthetic division. The polynomial is $-x^3 + 4x^2 + 0x - 8$ . Coefficients are $-1$ , $4$ , $0$ , $-8$ .
Set Up Table: Set up the synthetic division table using the root of the divisor $x - 2$ , which is $2$ . Place $2$ outside the table and $-1$ , $4$ , $0$ , $-8$ inside the table as the row of coefficients.
Begin Synthetic Division: Begin synthetic division: Bring down the first coefficient $-1$ directly below the line. Multiply it by $2$ (the root) to get $-2$ . Add this to the next coefficient $4$ to get $2$ . Write $2$ below the line.
Multiply and Add: Multiply the $2$ (just obtained) by $2$ (the root) to get $4$ . Add this to the next coefficient ( $0$ ) to get $4$ . Write $4$ below the line.
Calculate Remainder: Multiply the $4$ (just obtained) by $2$ (the root) to get $8$ . Add this to the next coefficient ( $-8$ ) to get $0$ . Write $0$ below the line. This is the remainder.
Final Result: The numbers below the line now represent the coefficients of the quotient and the remainder. The quotient is $-x^2 + 2x + 4$ and the remainder is $0$ .