Question

According to the synthetic division below, which of the following statements are true? Check all that apply. -5(2 6 -8) -10 20 ____________ 2 -4 12 A. When (2x2 + 6x - 8) is divided by (x + 5), the remainder is 12. B. When x = -5, 2x2 + 6x - 8 = 12. C. (x + 5) is a factor of 2x2 + 6x - 8. D. When x = 5, 2x2 + 6x - 8 = 12. E. (x - 5) is a factor of 2x2 + 6x - 8. F. When (2x2 + 6x - 8) is divided by (x - 5), the remainder is 12.

Answer 1

***(2x²+6x-8):(x+5)=2x-4
     -2x²-10x
    ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
         -4x-8
          4x+20
    ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
              12 ⇒ A. statement is true.

***When x=-5⇒2*(-5)²+6*(-5)-8=12⇒B. statement is true.

***2x²+6x-8 can also be written as (x+5)*(2x-4)+12 so (x+5) is a factor of 2x²+6x-8⇒C. statement is true.

***When x=5⇒2*5²+6*5-8=72 is not 12⇒D. statement is not true

***(2x²+6x-8):(x+5)=2x+16
     -2x²+10x
    ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
              16x-8
             -16x+80
        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
                     72⇒F. statement is not true

***E. statement is not true.

Answer 2

The correct answer is A and B