Questions: Factor the trinomial completely. x^2+4x-21

Transcript text: Factor the trinomial completely. \[ x^{2}+4 x-21 \]

Solution

Solution Steps

To factor the trinomial \(x^2 + 4x - 21\), we need to find two numbers that multiply to -21 (the constant term) and add up to 4 (the coefficient of the linear term). Once we find these numbers, we can rewrite the middle term and factor by grouping.

Step 1: Identify the Trinomial

We start with the trinomial \(x^2 + 4x - 21\).

Step 2: Factor the Trinomial

To factor the trinomial, we look for two numbers that multiply to \(-21\) (the constant term) and add to \(4\) (the coefficient of the linear term). The numbers that satisfy these conditions are \(-3\) and \(7\).

Step 3: Write the Factored Form

Using the identified numbers, we can express the trinomial in its factored form: \[ x^2 + 4x - 21 = (x - 3)(x + 7) \]