Question

According to the synthetic division below, which of the following statements are true? Check all that apply.
-6)2 9 -12 2 -3 11

A. When x = -6,2x2 + 9x-7 = 11.
B. When x = 6,2x2 + 9x-7 = 11.
C. (x-6) is a factor of 2x + 9x- 7.
D. When (2x + 9x-7) is divided by (x - 6), the remainder is 11.
E. When (2x2 + 9x - 7) is divided by (x + 6), the remainder is 11. F. (x+6) is a factor of 2x2 + 9x-7.​

Answer 1

The last number on a synthetic division represents the remainder of the division.

The true statements are:

• (a). When x = -6, 2x^2 + 9x - 7 = 11.
• (e). When (2x2 + 9x - 7) is divided by (x + 6), the remainder is 11.

From the question, we have the dividend to b 2x^2 + 9x - 7, the last number to be 11, and the zero of the divisor to be -6.

This means that:

$x = -6$ --- the divisor

Set to 0

$x+6 = 0$

So, when the dividend 2x^2 + 9x - 7 is divided by divisor x + 6, the remainder is 11.

This also means that, when -6 is substituted for x in the dividend, the remainder is 11

Hence, the true statements are (a) and (e)

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