Use synthetic division to find (x^2 + 12x + 11) ÷ (x + 1). 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 coefficients of the dividend (1 for x^2, 12 for x, and 11 for the constant term) and the root of the divisor, which is -1 for (x + 1).Perform synthetic division: Perform synthetic division: -1 | 1 12 11 | -1 -11 ------------ 1 11 0Write result of synthetic division: Write the result of synthetic division as a polynomial plus remainder over divisor: q(x) = 1x + 11 and the remainder r = 0.Check for remainder: Since the remainder is 0, the result is just the polynomial q(x) without any remainder term.

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Precalculus

Divide polynomials using synthetic division

Full solution

Q. Use synthetic division to find

(x^2 + 12x + 11) \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 by writing the coefficients of the dividend ( $1$ for $x^2$ , $12$ for $x$ , and $11$ for the constant term) and the root of the divisor, which is $-1$ for $(x + 1)$ .
Perform synthetic division: Perform synthetic division: $\newline$ $-1$ | $1$ $12$ $11$ $\newline$ | $-1$ $-11$ $\newline$ ------------ $\newline$ $1$ $11$ $0$
Write result of synthetic division: Write the result of synthetic division as a polynomial plus remainder over divisor: $q(x) = 1x + 11$ and the remainder $r = 0$ .
Check for remainder: Since the remainder is $0$ , the result is just the polynomial $q(x)$ without any remainder term.