Identify the constant term and the coefficient of the x term.

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3.3 Julie wants to factorize the following trinomial $x^2 + 9x + 20$ .

Identify the constant term and the coefficient of the $x$ term.
The trinomial is $x^2 + 9x + 20$ .
The constant term is 20.
The coefficient of the $x$ term is 9.
Find two numbers that multiply to the constant term and add to the coefficient of the $x$ term.
We need two numbers that multiply to 20 and add up to 9.
Let's list factors of 20:
- $1 \times 20 = 20$ , $1 + 20 = 21$
- $2 \times 10 = 20$ , $2 + 10 = 12$
- $4 \times 5 = 20$ , $4 + 5 = 9$ The two numbers are 4 and 5.

Write the trinomial in factored form.

Using the two numbers found, the trinomial can be factored as $(x+4)(x+5)$ .
The factored form is $\boxed{(x+4)(x+5)}$ .

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	$2(x^2 + 5x + 6)$
$-5a^2 - 15a - 10$	$\mathbf{-5}$	$\mathbf{-5(a^2 + 3a + 2)}$
$c^3 - 8c^2 + 15c$	$\mathbf{c}$	$\mathbf{c(c^2 - 8c + 15)}$

3.4.2 In the table below, the mathematical steps to factorize the trinomial has been provided. Provide an explanation for each step.

Step	Mathematical steps	Explanation
1	$3(x^3 - x^2 - 30x)$	Factor out 3 which is common.
2	$3x(x^2 - x - 30)$	Factor out the common factor $x$ from the terms inside the parenthesis.

Identify the constant term and the coefficient of the x term.

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