Question

Help me please right now! thank you guys so much

Answer 1

C

Explanation:

`(12x^3-14x^2-40x)/(2x-5)` ( factorise numerator by factoring out 2x from each term )

12x³ - 14x² - 40x

= 2x(6x² - 7x - 20) ← factor the quadratic

Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 20 = - 120 and sum = - 7

The factors are - 15 and + 8

Use these factors to split the x- term

6x² - 15x + 8x - 20 ( factor the first/second and third/fourth terms )

= 3x(2x - 5) + 4(2x - 5) ← factor out (2x - 5) from each term

= (2x - 5)(3x + 4)

Then

`(2x(2x-5)(3x+4))/(2x-5)` ← cancel the common factor (2x - 5) on numerator/denominator

= 2x(3x + 4) ← distribue

= 6x² + 8x → C