Question

factor trinomials (a=1)
score: 1/3 penalty: 0.25 off
question
factor.
$x^2 + 4x - 21$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-21\) and add up to \(4\). Let's list the factor pairs of \(-21\): \((-1, 21)\), \((1, -21)\), \((-3, 7)\), \((3, -7)\). Among these, \(-3\) and \(7\) add up to \(4\) (since \(-3 + 7 = 4\)) and multiply to \(-21\) (since \(-3\times7=-21\)).

Step2: Factor the trinomial

Using the numbers we found, we can factor the trinomial \(x^{2}+4x - 21\) as \((x - 3)(x + 7)\) because when we expand \((x - 3)(x + 7)\) using the distributive property (FOIL method), we get \(x^{2}+7x-3x - 21=x^{2}+4x - 21\), which matches the original trinomial.

Answer:

\((x - 3)(x + 7)\)