Complete the table by identifying the common factor in each trinomial and then writing the trinomial by factoring out the common factor.

here are the solutions to the factorization problems:

3.4.1 Complete the table below by identifying the common factor in each trinomial and then writing the trinomial by factoring out the common factor.

Trinomial	What is the common factor?	Write the trinomial with the Common Factor factored out.
$2x^2 + 10x + 12$	2	$2(x^2 + 5x + 6)$
$-5a^2 - 15a - 10$	$\boxed{-5}$	$\boxed{-5(a^2 + 3a + 2)}$
$c^3 - 8c^2 + 15c$	$\boxed{c}$	$\boxed{c(c^2 - 8c + 15)}$

3.4.2 In the table below, the mathematical steps to factorize the trinomial has been provided. Provide an explanation for each step.
Factorize $3x^3 - 3x^2 - 90x$.

Step	Mathematical steps	Explanation
1	$3(x^3 - x^2 - 30x)$	Factor out 3 which is common.
2	$3x(x^2 - x - 30)$	$\boxed{\text{Factor out the common factor } x \text{ from the terms inside the parenthesis.}}$
3	$\boxed{3x(x - 6)(x + 5)}$	$\boxed{\text{Factor the quadratic trinomial } x^2 - x - 30.}$