Problem 22 - College Algebra Essentials

Question

Factor each trinomial, or state that the trinomial is prime. $$x^{2}-14 x+45$$

Step-by-Step Solution

Answer

The factored form of the trinomial \(x^{2}-14x+45\) is \((x-5)(x-9)\).

Step 1: Listing down the factors of the constant term

List down the pairs of factors of 45: (1, 45), (-1, -45), (3, 15), (-3, -15), (5,9) and (-5, -9).

Step 2: Finding the pair of factors

Find the pair of factors that add up to -14, the coefficient of the 'x' term. The pair (-5, -9) has a sum of -14.

Step 3: Writing the factored form

Write the factors as binomials. The trinomial \(x^{2}-14x+45\) therefore factors to \((x-5)(x-9)\).