Question

factor the expression completely.
15x² - 25x - 60
15x² - 25x - 60 = \square

Explanation:

Step1: Factor out GCF

The greatest common factor of $15x^2$, $-25x$, and $-60$ is 5.
$15x^2 -25x -60 = 5(3x^2 -5x -12)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $3\times(-12)=-36$ and add to $-5$. These numbers are $-9$ and $4$. Split the middle term and factor by grouping:
$3x^2 -5x -12 = 3x^2 -9x +4x -12 = 3x(x-3)+4(x-3)=(3x+4)(x-3)$

Step3: Combine factors

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

Answer:

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