Questions: Factor: x^2 + 4x - 21

Solution Steps

To factor the quadratic expression \(x^2 + 4x - 21\), we need to find two numbers that multiply to the constant term (-21) and add up to the coefficient of the linear term (4). Once we find these numbers, we can rewrite the quadratic expression in its factored form.

We start with the quadratic expression: \[ x^2 + 4x - 21 \]

We need to find two numbers that multiply to \(-21\) (the constant term) and add up to \(4\) (the coefficient of the linear term). These numbers are \(-3\) and \(7\).

Using the numbers \(-3\) and \(7\), we can rewrite the quadratic expression as: \[ (x - 3)(x + 7) \]

Final Answer