Question

use synthetic division to find $(x^{2} + 8x + 24) \div (x + 2)$. 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.

Explanation:

-2: $1 \times (-2) = -2$. Add to 8: $8 + (-2) = 6$. Multiply 6 by -2: $6 \times (-2) = -12$. Add to 24: $24 + (-12) = 12$.

Step4: Form result

Quotient $q(x) = x + 6$, remainder $r = 12$, divisor $d(x) = x + 2$. So the result is $x + 6 + \frac{12}{x + 2}$.

Answer:

-2: $1 \times (-2) = -2$. Add to 8: $8 + (-2) = 6$. Multiply 6 by -2: $6 \times (-2) = -12$. Add to 24: $24 + (-12) = 12$.

Step4: Form result

Quotient $q(x) = x + 6$, remainder $r = 12$, divisor $d(x) = x + 2$. So the result is $x + 6 + \frac{12}{x + 2}$.