Question

use synthetic division to find the result when $4x^3 - 17x^2 + 14x + 8$ is divided by $x - 2$.

Explanation:

Step1: Set up synthetic division

Root divisor: $2$, coefficients: $4, -17, 14, 8$

Step2: Bring down leading coefficient

$\downarrow \quad \quad \quad \quad \quad$
$4$

Step3: Multiply and add column 1

$2 \times 4 = 8$; $-17 + 8 = -9$
$4 \quad -9$

Step4: Multiply and add column 2

$2 \times (-9) = -18$; $14 + (-18) = -4$
$4 \quad -9 \quad -4$

Step5: Multiply and add column 3

$2 \times (-4) = -8$; $8 + (-8) = 0$
$4 \quad -9 \quad -4 \quad 0$

Step6: Form quotient polynomial

Degree reduces by 1: $4x^2 -9x -4$, remainder $0$

Answer:

$4x^2 - 9x - 4$