Use synthetic division to find (3x^2 - x - 24) ÷ (x - 3). Write your answer in the form q(x) + r/d(x), where q(x) is a polynomial, r is an integer, and d(x) is a linear polynomial. Simplify any fractions. ______

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 -24 and 24 to get 0.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) + r/d(x). Since the remainder is 0, the result is just the quotient 3x + 8.

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Precalculus

Divide polynomials using synthetic division

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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 $3x + 8$ .