Problem 20 - Algebra and Trigonometry

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: Set up the equation

The trinomial being asked to factor is \(x^{2}-4x-5\).

Step 2: Finding the factor pair

Look for two numbers that multiply together to give -5, and at the same time, add together to give -4. After analyzing, it can be concluded that -5 and 1 are the required pair. These two numbers multiply to -5 and add to -4.

Step 3: Write the answer

Having obtained the pair of numbers, rewrite the trinomial in its factored form using \(x - a)(x - b)\) where \(a\) and \(b\) are the numbers found in the previous step. Therefore, the factored form of the given trinomial is \((x - 5)(x + 1)\).