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Use synthetic division to find $(x^2 + 8x - 7) \div (x - 1)$ . $\newline$ 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 - 7) \div (x - 1)

.

\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 $(x - 1)$ , which is $1$ , and the coefficients of the dividend $(x^2 + 8x - 7)$ , which are $1$ , $8$ , and $-7$ .
Perform synthetic division: Perform synthetic division: $\newline$ $1 | 1\ 8\ -7$ $\newline$ $|\ 1\ 9$ $\newline$ $------------$ $\newline$ $1\ 9\ 2$
Write result polynomial: Write the result of the synthetic division as a polynomial plus a remainder: $q(x) = x + 9$ and the remainder is $2$ .
Express result in form: Express the result in the form $q(x) + \frac{r}{d(x)}$ : $(x + 9) + \frac{2}{(x - 1)}$ .

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