Question

4.

Use Synthetic Division To Solve.

(x3-3x2-7x+6) / (x-2)

A. x2+x+9+ 12 /x-2

B. x2+5x+3+ 12 / x-2

C. x2-5x+3

D. x2-x-9-12/x-2

Answer 1

D. x^2-x-9-12/x-2

Explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

2 | 1 -3 -7 6

|______2___-2__-18

| 1 -1 -9 -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).