Question

use synthetic division to find the result when $2x^3 - 7x^2 - 2x - 8$ is divided by $x - 4$.

Explanation:

Step1: Set up synthetic division

Root: $4$, Coefficients: $2, -7, -2, -8$

Step2: Bring down leading coefficient

$\downarrow \quad 2$

Step3: Multiply and add column 1

$4 \times 2 = 8$; $-7 + 8 = 1$

Step4: Multiply and add column 2

$4 \times 1 = 4$; $-2 + 4 = 2$

Step5: Multiply and add column 3

$4 \times 2 = 8$; $-8 + 8 = 0$

Step6: Write quotient polynomial

Result: $2x^2 + 1x + 2$ (remainder $0$)

Answer:

$2x^2 + x + 2$