Question

Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table. What is the value of f(2)? −14 −11 −2 −1 A synthetic division setup with respective columns containing the following numbers column 1 containing two as a divisor, column 2 containing negative 1, blank and negative 1, column 3 containing negative 5, negative 2, negative 7, and column 4 containing three, negative 14, negative 11.There is a line above the numbers negative 1, negative 7 and negative 11.

Answer 1

-11 is correct for all future users.

Explanation:

Answer 2

-11

Explanation:

The answer to the first one sould be -11

2x^3 +5x^2−x−6

Write 5x^2 as 4x^2 + x^2......and we have.....

2x^3 + 4x^2 + x^2 - x - 6

2x^2 ( x + 2) + ( x + 2)(x - 3)

(x + 2) [ 2x^2 + x - 3]

(x + 2) (2x +3) (x - 1)

x^3−4x^2−3x+18 = 0

Using some synthetic division, we have

3 [ 1 - 4 -3 18 ]

3 -3 -18

_______________

1 -1 -6 0

The remaining polynomial is x^2 - x - 6 which factors as (x - 3) ( x + 2)

So .... the factored form is (x - 3) ( x - 3) ( x + 2) = ( x + 2) ( x - 3)^2 = 0