Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one!

Question

x^2 + x - 12

Answer 1

To factor the quadratic expression \( x^2 + x - 12 \), we need to find two numbers that multiply to \(-12\) (the constant term) and add to \(1\) (the coefficient of the linear term \(x\)).

The two numbers that meet these criteria are \(4\) and \(-3\) since:

• \(4 \times (-3) = -12\)
• \(4 + (-3) = 1\)

Thus, we can factor the expression as follows:

\[ (x + 4)(x - 3) \]

So, the factored form of \( x^2 + x - 12 \) is \((x + 4)(x - 3)\).