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

Answer:

-11

Step-by-step 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