Problem 20 - College Algebra Essentials

Question

Factor each trinomial, or state that the trinomial is prime. $$x^{2}-4 x-5$$

Step-by-Step Solution

Answer

The factored form of the trinomial \( x^{2}-4x-5 \) is \( (x - 5)(x + 1) \)

Step 1: Find two numbers

Find two numbers that multiply together to give -5 (the constant term) and add together to get -4 (the coefficient of the x term). The numbers that satisfy these conditions are -5 and 1, since -5 * 1 = -5 and -5 + 1 = -4.

Step 2: Write the factored form

Having identified these numbers, write the trinomial in its factored form. That would be \( (x - 5)(x + 1) \). This is because when multiplying these two binomial terms (using the FOIL method - First, Outer, Inner, Last), we get back the original trinomial \( x^{2}-4x-5 \)

Step 3: Check the factored form

It's always good to check your factored form by expanding it out. That means applying the FOIL rule to \( (x - 5)(x + 1) \) . This confirms the factored form is correct as it matches the original trinomial \( x^{2}-4x-5 \)