(x%5E2-9)-factor.jpeg "(x^2-5x+4)(x^2-9) Factor")
Factoring the Expression: (x² - 5x + 4)(x² - 9)
This expression involves two factors: (x² - 5x + 4) and (x² - 9). We can factor each of them separately to get the fully factored expression.
Factoring (x² - 5x + 4)
- This is a quadratic expression. We need to find two numbers that add up to -5 (the coefficient of the x term) and multiply to 4 (the constant term).
- The numbers -4 and -1 satisfy these conditions: (-4) + (-1) = -5 and (-4) * (-1) = 4.
- Therefore, we can rewrite (x² - 5x + 4) as (x - 4)(x - 1).
Factoring (x² - 9)
- This expression is a difference of squares, which has the general form a² - b².
- In this case, a = x and b = 3.
- The difference of squares factors into (a + b)(a - b).
- So, (x² - 9) factors into (x + 3)(x - 3).
Combining the Factors
Now we have factored both parts of the original expression:
- (x² - 5x + 4) = (x - 4)(x - 1)
- (x² - 9) = (x + 3)(x - 3)
Combining them, we get the fully factored expression:
(x - 4)(x - 1)(x + 3)(x - 3)
This is the factored form of the expression (x² - 5x + 4)(x² - 9).