Question

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factor the expression $x^2 + 4x - 12$.
enter the correct answer in the box.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-12\) and add up to \(4\). Let's list the factor pairs of \(-12\): \((-1, 12)\), \((1, -12)\), \((-2, 6)\), \((2, -6)\), \((-3, 4)\), \((3, -4)\). Among these, \(-2\) and \(6\) multiply to \(-12\) (\(-2\times6 = -12\)) and add up to \(4\) (\(-2 + 6 = 4\)).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}+4x - 12\) as \((x - 2)(x + 6)\) because when we expand \((x - 2)(x + 6)\) using the distributive property (FOIL method), we get \(x^{2}+6x - 2x - 12=x^{2}+4x - 12\), which matches the original expression.

Answer:

\((x - 2)(x + 6)\)