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Use synthetic division to find $(x^2 + 8x - 3) \div (x - 2)$ . $\newline$ 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

(x^2 + 8x - 3) \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 with the root of the divisor $(x - 2)$ , which is $2$ , and the coefficients of the dividend $(x^2 + 8x - 3)$ , which are $1$ , $8$ , and $-3$ .
Perform synthetic division: Perform synthetic division: $\newline$ $2$ | $1$ $8$ $-3$ $\newline$ | $2$ $20$ $\newline$ ------------ $\newline$ $1$ $10$ $17$
Write the result: Write the result of the synthetic division. The quotient is $x + 10$ and the remainder is $17$ .
Express the result: Express the result in the form $q(x) + \frac{r}{d(x)}$ . The quotient $q(x)$ is $x + 10$ , the remainder $r$ is $17$ , and the divisor $d(x)$ is $x - 2$ .

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