Question

factor the expression completely
15x² - 50x - 40
15x² - 50x - 40 = □

Explanation:

Step1: Factor out GCF

The greatest common factor of 15, 50, and 40 is 5.
$15x^2 - 50x - 40 = 5(3x^2 - 10x - 8)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $3\times(-8)=-24$ and add to $-10$. These numbers are $-12$ and $2$. Split the middle term and factor:
$3x^2 - 10x - 8 = 3x^2 - 12x + 2x - 8 = 3x(x-4) + 2(x-4) = (3x+2)(x-4)$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1.
$5(3x+2)(x-4)$

Answer:

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