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Your answer should be in the form $p(x)+\frac{k}{x+3}$ where $p$ is a polynomial and $k$ is an integer. $\frac{x^2+5x+5}{x+3}$

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Divide polynomials using synthetic division

Full solution

Q. Your answer should be in the form

p(x)+\frac{k}{x+3}

where

p

is a polynomial and

k

is an integer.

\frac{x^2+5x+5}{x+3}

Identify Polynomial and Divisor: Identify the polynomial and divisor from the given expression $(x^2+5x+5)/(x+3)$ .
Perform Long Division: Perform polynomial long division of $x^2 + 5x + 5$ by $x + 3$ .
Write Result: Write the result of the division. The quotient is $x + 2$ and the remainder is $-1$ .
Express in Form: Express the original expression in the form $p(x) + \frac{k}{x+3}$ . Here, $p(x) = x + 2$ and $k = -1$ .

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