Problem 19 - Introductory Algebra for College Students

Question

Factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$x^{2}-2 x-8$$

Step-by-Step Solution

Answer

The factored form of the trinomial is \( (x - 4)(x + 2)\).

Step 1: Factor the Trinomial

Identify two numbers that both add to -2 and multiply to -8. These numbers are -4 and 2. So, the trinomial \(x^{2}-2 x-8\) can be factored as \( (x - 4)(x + 2)\).

Step 2: FOIL Check

Verify the factorization by applying the FOIL rule. Multiplying the terms: First terms: \(x * x = x^2\), Outer terms: \(x * 2 = 2x\), Inner terms: \(-4 * x = -4x\), Last terms: \(-4 * 2 = -8\). Combining like terms results in \(x^2 - 2x - 8\) which matches the original trinomial, confirming that the factorization is correct.