Question

factor trinomials (a=1)
score: 2/5 penalty: 1 off
question
factor:
$x^2 + 2x - 24$
answer
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Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-24\) (the constant term) and add up to \(2\) (the coefficient of \(x\)). Let's list the factor pairs of \(-24\): \((-1, 24)\), \((1, -24)\), \((-2, 12)\), \((2, -12)\), \((-3, 8)\), \((3, -8)\), \((-4, 6)\), \((4, -6)\). Among these, the pair \(6\) and \(-4\) works because \(6\times(-4)=-24\) and \(6 + (-4)=2\).

Step2: Factor the trinomial

Using the numbers we found, we can factor \(x^{2}+2x - 24\) as \((x + 6)(x - 4)\) because when we expand \((x + 6)(x - 4)\) using the distributive property (FOIL method), we get \(x^{2}-4x + 6x - 24=x^{2}+2x - 24\), which matches the original trinomial.

Answer:

\((x + 6)(x - 4)\)