Question

use synthetic division to find ((x^{2}+9x - 39)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:

Step1: Set up synthetic division

Root of divisor $x-2$ is $2$. Coefficients of dividend $x^2+9x-39$ are $1, 9, -39$.

2 | 1   9   -39
      2   22
  -------------

Step2: Calculate row sums

Bring down 1. Multiply by 2, add to 9: $9+2=11$. Multiply 11 by 2, add to -39: $-39+22=-17$.

2 | 1   9   -39
      2   22
  -------------
    1  11  -17

Step3: Identify quotient and remainder

Quotient $q(x)$ is $x+11$, remainder $r=-17$, divisor $d(x)=x-2$.

Answer:

$x + 11 + \frac{-17}{x - 2}$ or $x + 11 - \frac{17}{x - 2}$