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Use synthetic division to find $(x^2 + 6x - 28) \div (x + 5)$ . $\newline$ 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 + 6x - 28) \div (x + 5)

.

\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 $-5$ (the root of $x + 5$ ) and the coefficients of the polynomial $x^2 + 6x - 28$ , which are $1$ , $6$ , and $-28$ .
Perform synthetic division: Perform synthetic division: $\newline$ $-5$ | $1$ $6$ $-28$ $\newline$ | $-5$ $-5$ $\newline$ ------------ $\newline$ $1$ $1$ $-33$
Write result as polynomial: Write the result of synthetic division as a polynomial plus a remainder: $q(x) = 1x + 1$ and the remainder is $-33$ .
Express result in form: Express the result in the form $q(x) + \frac{r}{d(x)}$ : $q(x) = x + 1$ and $\frac{r}{d(x)} = -\frac{33}{x + 5}$ .
Simplify the fraction: Simplify the fraction if possible. Since $-33/(x + 5)$ cannot be simplified further, this is the final form.

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