Question

1. factor: 6x² - 15x - 36

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of the coefficients 6, - 15, and - 36. The GCF of 6, 15, and 36 is 3.
$6x^{2}-15x - 36=3(2x^{2}-5x - 12)$

Step2: Factor the quadratic expression inside the parentheses

For the quadratic expression $2x^{2}-5x - 12$, we need to find two numbers that multiply to $2\times(-12)=-24$ and add up to - 5. The numbers are - 8 and 3.
$2x^{2}-5x - 12=2x^{2}-8x+3x - 12$

Step3: Group the terms

Group the terms of $2x^{2}-8x+3x - 12$:
$(2x^{2}-8x)+(3x - 12)$

Step4: Factor out the common factors from each group

Factor out the common factors from each group:
$2x(x - 4)+3(x - 4)$

Step5: Factor out the common binomial factor

Factor out the common binomial factor $(x - 4)$:
$(x - 4)(2x+3)$

So, $6x^{2}-15x - 36=3(x - 4)(2x+3)$

Answer:

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