Julie wants to factorize the following trinomial x2 + 9x + 20, provide her with 3 easy steps to follow.

Question

ScanSolve AI Tutor · Accepted Answer

Okay Mfu, let's continue with these factoring problems.

3.3
To factorize the trinomial $x^2 + 9x + 20$ , Julie can follow these 3 easy steps:

Find two numbers that multiply to the constant term (20) and add up to the coefficient of the middle term (9).
The two numbers are 4 and 5, because $4 \times 5 = 20$ and $4 + 5 = 9$ .
Rewrite the middle term ($9x$) using these two numbers.
$x^2 + 4x + 5x + 20$

Group the first two terms and the last two terms, then factor out the greatest common factor (GCF) from each group.

(x^2 + 4x) + (5x + 20)

x(x + 4) + 5(x + 4)

Now, factor out the common binomial factor $(x + 4)$ .

(x + 4)(x + 5)

The factored expression is $\boxed{(x + 4)(x + 5)}$ .

3.4.1
Let's complete the table by identifying the common factor and writing the trinomial with the common factor factored out.

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
Here are the explanations for the mathematical steps to factorize $3x^3 - 3x^2 - 90x$ :

| Step | Mathematical steps | Explanation

Step-by-step solution