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(x^2-5x+4)(x^2-9) Factor

2 min read Jun 17, 2024
(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).

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