Question

According to the synthetic division below, which of the following statements
are true?
Check all that apply.
-62
9
-12
-7
18
2
-3
11
O A. (x-6) is a factor of 2x2 + 9x-7.
B. (x+6) is a factor of 2x2 + 9x-7.
C. When (2x2 + 9x - 7) is divided by (x - 6), the remainder is 11.
D. When (2x2 + 9x - 7) is divided by (x + 6), the remainder is 11.
E. When x = -6, 2x2 + 9x- 7 = 11.
F. When x = 6, 2x2 + 9x - 7 = 11.

Answer 1

Using synthetic division, it is found that the correct options are:

• C. When $2x^2 + 9x - 7$ is divided by $x - 6$, the remainder is 11.

• E. When $x = -6, 2x^2 + 9x - 7 = 11$.

In this problem:

• The polynomial $p(x) = 2x^2 + 9x - 7$.

• It is divided by $x + 6$.

• The result is $2x - 3$.

• The remainder is 11.

Also, when x = -6, we have that:

$p(-6) = 2(-6)^2 + 9(-6) - 7 = 72 - 54 - 7 = 11$

Hence, options C and E are correct.

To learn more about synthetic division, you can take a look at https://brainly.com/question/24662212