Question

use synthetic division to divide (6x^3 - 10x^2 + 20) by (x + 1).
a. (6x^2 - 16x + 16 + \frac{4}{x + 1})
b. (6x^2 - x + 16 + \frac{6}{x + 1})
c. (6x^2 - 16x + 16 - \frac{4}{x + 1})
d. (6x^2 - 16x - 16 + \frac{5}{x + 1})

Explanation:

Step1: Identify root for divisor

For $x+1=0$, root is $x=-1$.
Coefficients of dividend: $6, -10, 0, 20$ (0 for missing $x$ term)

Step2: Set up synthetic division

$$\begin{array}{r|rrrr} -1 & 6 & -10 & 0 & 20 \\ \hline & & -6 & 16 & -16 \\ \hline & 6 & -16 & 16 & 4 \end{array}$$

Step3: Write quotient and remainder

Quotient: $6x^2-16x+16$, Remainder: $4$
Result: $6x^2-16x+16+\frac{4}{x+1}$

Answer:

A. $6x^{2}-16x + 16+\frac{4}{x + 1}$