(x%5E2-9)%3D-factor-completely.jpeg "(x^2-5x+4)(x^2-9)= Factor Completely")
Factoring the Expression (x² - 5x + 4)(x² - 9)
This problem involves factoring a product of two quadratic expressions. Let's break it down step-by-step.
Step 1: Factor each quadratic expression
- (x² - 5x + 4): This expression can be factored into (x - 1)(x - 4).
- (x² - 9): This is a difference of squares, which factors into (x + 3)(x - 3).
Step 2: Combine the factored expressions
Now that we have factored each quadratic, we can combine them to get the completely factored expression:
(x² - 5x + 4)(x² - 9) = (x - 1)(x - 4)(x + 3)(x - 3)
Final answer
Therefore, the completely factored form of the expression (x² - 5x + 4)(x² - 9) is (x - 1)(x - 4)(x + 3)(x - 3).