Answer:
C
Step-by-step explanation:
[tex]\frac{12x^3-14x^2-40x}{2x-5}[/tex] ( 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
[tex]\frac{2x(2x-5)(3x+4)}{2x-5}[/tex] ← cancel the common factor (2x - 5) on numerator/denominator
= 2x(3x + 4) ← distribue
= 6x² + 8x → C
