Question

Monserrat was asked to create an equivalent form of the rational expression 8x2+2x−142x+3
. Which of the following is a correct equivalent form?(1 point)

4x−5+18x2+2x−14

4x+7+72x+3

4x−5+12x+3

4x+14

Answer 1

Divide 8x^2 + 2x − 14 by 2x + 3:

- 8x^2 ÷ 2x = 4x → 4x(2x+3) = 8x^2 + 12x
Subtract: (8x^2+2x−14) − (8x^2+12x) = −10x − 14

- (−10x) ÷ 2x = −5 → −5(2x+3) = −10x −15
Subtract: (−10x−14) − (−10x−15) = 1 (remainder)

So (8x^2 + 2x − 14)/(2x + 3) = 4x − 5 + 1/(2x + 3).

That corresponds to option 3.