Question

factor trinomials (a=1)
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question
factor.
$x^2 + 12x + 32$
answer
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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 \(32\) (sum \(33\)), \(2\) and \(16\) (sum \(18\)), \(4\) and \(8\) (sum \(12\)). So the numbers are \(4\) and \(8\).

Step2: Factor the trinomial

Using the formula \(x^{2}+bx + c=(x + m)(x + n)\) where \(m\) and \(n\) are the two numbers we found, we substitute \(m = 4\) and \(n = 8\). So \(x^{2}+12x + 32=(x + 4)(x + 8)\).

Answer:

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