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Use synthetic division to find $(3x^2 - x - 24) \div (x - 3)$ . $\newline$ 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

(3x^2 - x - 24) \div (x - 3)

.

\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 with the root of the divisor $x - 3$ , which is $3$ , and the coefficients of the dividend $3x^2 - x - 24$ , which are $3$ , $-1$ , and $-24$ .
Perform synthetic division: Perform synthetic division: Bring down the leading coefficient $3$ . Multiply $3$ by the root $3$ to get $9$ . Add $-1$ and $9$ to get $8$ . Multiply $8$ by the root $3$ to get $24$ . Add $3$ $0$ and $24$ to get $3$ $2$ .
Write the result: Write the result of synthetic division. The quotient is $3x + 8$ and the remainder is $0$ .
Express the result: Express the result in the form $q(x) + \frac{r}{d(x)}$ . Since the remainder is $0$ , the result is just the quotient $3x + 8$ .

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