Question

use synthetic division to find the result when $3x^3 - 8x^2 + 12x - 16$ is divided by $x - 2$. if there is a remainder, express the result in the form $q(x) + \frac{r(x)}{b(x)}$.

Explanation:

Step1: Set up synthetic division

Root divisor: $x=2$, coefficients: $3, -8, 12, -16$

Step2: Bring down leading coefficient

$\downarrow \quad \quad \quad \quad \quad \quad$
$3$

Step3: Multiply and add column 1

$3 \times 2 = 6$; $-8 + 6 = -2$

Step4: Multiply and add column 2

$-2 \times 2 = -4$; $12 + (-4) = 8$

Step5: Multiply and add column 3

$8 \times 2 = 16$; $-16 + 16 = 0$

Step6: Write quotient and remainder

Quotient: $3x^2 - 2x + 8$, remainder: $0$

Answer:

$3x^2 - 2x + 8$