Use synthetic division to find (x^2 + 8x - 3) ÷ (x - 2). 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 - 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: 2 | 1 8 -3 | 2 20 ------------ 1 10 17Write 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) + 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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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 $x - 2$ .