Question

According to the synthetic division below, which of the following statements are true?

Answer 1

Answer:

Options (A) and (D)

Step-by-step explanation:

We can write the given division as,

$\frac{2x^2+6x-8}{x+5}=2x-4+\frac{12}{x+5}$

Option (A)

When (2x² + 6x - 8) is divided (x + 5), the remainder is 12.

True.

Option (B)

When (2x² + 6x - 8) is divided (x - 5), the remainder is 12.

False.

Option (C)

When x = 5,

2x² + 6x - 8 = 12

2(5)² + 6(5) - 8 = 50 + 30 - 8

                        = 72

False.

Option (D)

When x = -5,

2(-5)² + 6(-5) - 8 = 50 - 30 - 8

                          = 12

True.

Option (E)

(x - 5) is a factor of 2x² + 6x - 8

If (x - 5) is a factor value of 2x² + 6x - 8 should be zero.

False.

Option (F)

(x + 5) is a factor of 2x² + 6x - 8

If (x + 5) is a factor then by substituting x = -5 in the expression value should be zero.

But the value is 12.

False.