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