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Use synthetic division to find $(8x^2 + 24x + 16) \div (x + 2)$ . $\newline$ Write your answer in the form $q(x) + \frac{r}{d(x)}$ , where $q(x)$ is a polynomial, $r$ is an integer, and $d(x)$ is a linear polynomial. Simplify any fractions. $\newline$ _________

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Divide polynomials using synthetic division

Full solution

Q. Use synthetic division to find

(8x^2 + 24x + 16) \div (x + 2)

.

\newline

Write your answer in the form

q(x) + \frac{r}{d(x)}

, where

q(x)

is a polynomial,

r

is an integer, and

d(x)

is a linear polynomial. Simplify any fractions.

\newline

_________

Set up synthetic division: Set up synthetic division by writing the root of the divisor $(x + 2)$ as $-2$ and the coefficients of the dividend $(8x^2 + 24x + 16)$ as $8$ , $24$ , and $16$ .
Perform synthetic division: Perform synthetic division: $\newline$ $-2$ | $8$ $24$ $16$ $\newline$ | $-16$ $-16$ $\newline$ ------------- $\newline$ $8$ $8$ $0$
Write result of synthetic division: Write the result of synthetic division as a polynomial plus a remainder: $q(x) = 8x + 8$ and the remainder is $0$ .
Check for remainder: Since the remainder is $0$ , the result is just the polynomial $q(x)$ without any remainder term.

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