Question

question
use synthetic division to find the result when $x^4 - 4x^3 - 16x^2 + 22x + 18$ is divided by $x - 6$. if there is a remainder, express the result in the form $q(x) + \frac{r(x)}{b(x)}$.
answer
attempt 1 out of 2

Explanation:

Step1: Set up synthetic division

Divisor root: $6$, coefficients: $1, -4, -16, 22, 18$

6 | 1  -4  -16  22  18
        6   12  -24 -12
      ----------------

Step2: Calculate column sums

Bring down 1, multiply by 6, add to next coefficient:
$1$
$-4 + 6 = 2$
$-16 + (2\times6) = -16 + 12 = -4$
$22 + (-4\times6) = 22 - 24 = -2$
$18 + (-2\times6) = 18 - 12 = 6$

6 | 1  -4  -16  22  18
        6   12  -24 -12
      ----------------
      1   2   -4   -2   6

Step3: Identify quotient and remainder

Quotient degree = $4-1=3$, coefficients: $1,2,-4,-2$; remainder = $6$

Answer:

$x^3 + 2x^2 - 4x - 2 + \frac{6}{x-6}$