Question

factor trinomials (a=1)
score: 1/5 penalty: 1 off
question
factor.
$x^2 + 12x + 32$
answer

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(32\) (the constant term) and add up to \(12\) (the coefficient of \(x\)). Let's list the factor pairs of \(32\): \(1\) and \(32\), \(2\) and \(16\), \(4\) and \(8\). Checking the sums: \(4 + 8 = 12\).

Step2: Factor the trinomial

Using the two numbers \(4\) and \(8\), we can factor the trinomial \(x^{2}+12x + 32\) as \((x + 4)(x + 8)\) because when we expand \((x + 4)(x + 8)\) using the distributive property (FOIL method), we get \(x^{2}+8x+4x + 32=x^{2}+12x + 32\).

Answer:

\((x + 4)(x + 8)\)