Question

question
factor.
$x^2 + 4x - 45$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-45\) and add up to \(4\). Let's list the factor pairs of \(-45\): \((-1, 45)\), \((1, -45)\), \((-3, 15)\), \((3, -15)\), \((-5, 9)\), \((5, -9)\). The pair \(-5\) and \(9\) works because \(-5\times9 = -45\) and \(-5 + 9 = 4\).

Step2: Factor the quadratic

Using the two numbers we found, we can factor the quadratic as \((x - 5)(x + 9)\) because when we expand \((x - 5)(x + 9)\), we get \(x^2 + 9x - 5x - 45 = x^2 + 4x - 45\), which matches the original expression.

Answer:

\((x - 5)(x + 9)\)