Question

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: Identify root and coefficients

Root of divisor $x-2$ is $2$; coefficients of dividend: $3, -8, 12, -16$

Step2: Set up synthetic division

$$\begin{array}{r|rrrr} 2 & 3 & -8 & 12 & -16 \\ & & 6 & -4 & 16 \\ \hline & 3 & -2 & 8 & 0 \\ \end{array}$$

Step3: Write quotient and remainder

Quotient $q(x)=3x^2-2x+8$, remainder $r(x)=0$

Step4: Format final expression

Since remainder is 0, the result is the quotient.

Answer:

$3x^2 - 2x + 8$