Questions: Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". x^2+2x-24

Solution Steps

To factor the trinomial \(x^2 + 2x - 24\), we need to find two numbers that multiply to the constant term (-24) and add to the linear coefficient (2). If such numbers exist, we can express the trinomial as a product of two binomials. If not, the trinomial is not factorable over the integers.

We start with the trinomial \(x^2 + 2x - 24\).

To factor the trinomial, we look for two numbers that multiply to \(-24\) (the constant term) and add to \(2\) (the coefficient of the linear term). The numbers \(6\) and \(-4\) satisfy these conditions since: \[ 6 \times (-4) = -24 \quad \text{and} \quad 6 + (-4) = 2 \]

Using the identified numbers, we can express the trinomial in its factored form: \[ x^2 + 2x - 24 = (x - 4)(x + 6) \]

Final Answer