Questions: Factor completely. w^2 + 2w - 24

Solution Steps

To factor the quadratic expression \( w^2 + 2w - 24 \), we need to find two numbers that multiply to -24 (the constant term) and add up to 2 (the coefficient of the linear term). Once we find these numbers, we can rewrite the quadratic expression in its factored form.

We start with the quadratic expression: \[ w^2 + 2w - 24 \]

We need to find two numbers that multiply to \(-24\) (the constant term) and add up to \(2\) (the coefficient of the linear term).

The numbers that satisfy these conditions are \(6\) and \(-4\), since: \[ 6 \times (-4) = -24 \quad \text{and} \quad 6 + (-4) = 2 \]

Using these factors, we can rewrite the quadratic expression as: \[ w^2 + 2w - 24 = (w - 4)(w + 6) \]

Final Answer