Use synthetic division to find (x^2 + 3x + 2) ÷ (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 by writing the root of the divisor (x + 2) as -2 and the coefficients of the dividend (x^2 + 3x + 2) as 1, 3, and 2.Perform synthetic division: Perform synthetic division: -2 | 1 3 2 | -2 -2 ------------ 1 1 0 The new row of numbers represents the coefficients of the quotient polynomial and the remainder.Write quotient polynomial: Write the quotient polynomial using the new coefficients: q(x) = 1x + 1.Final answer: Since the remainder is 0, write the final answer as q(x) with no remainder: q(x) + r/d(x) = (x + 1) + 0/(x + 2).

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Precalculus

Divide polynomials using synthetic division

Full solution

Q. Use synthetic division to find

(x^2 + 3x + 2) \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 by writing the root of the divisor $(x + 2)$ as $-2$ and the coefficients of the dividend $(x^2 + 3x + 2)$ as $1$ , $3$ , and $2$ .
Perform synthetic division: Perform synthetic division: $\newline$ $-2$ \left|\begin{array}{ccc}$\newline1 & 3 & 2 (\newline$& -2 & -2 (\newline\)\hline $\newline$ 1 & 1 & 0 $\newline$ \end{array}\right.\) $\newline$ The new row of numbers represents the coefficients of the quotient polynomial and the remainder.
Write quotient polynomial: Write the quotient polynomial using the new coefficients: $q(x) = 1x + 1$ .
Final answer: Since the remainder is $0$ , write the final answer as $q(x)$ with no remainder: $q(x) + \frac{r}{d(x)} = (x + 1) + \frac{0}{(x + 2)}$ .