Question

1. factor: $6x^{2}-15x - 36$

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 and factor by grouping

Group the terms: $(2x^{2}-8x)+(3x - 12)$
Factor out the common factors from each group: $2x(x - 4)+3(x - 4)$
Then, factor out the common factor $(x - 4)$: $(x - 4)(2x+3)$

Step4: Combine with the GCF

Since we had factored out 3 in Step 1, the factored form of the original expression is $3(x - 4)(2x+3)$

Answer:

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