Rewrite the expression as a product of four linear factors: (x^(2)-9x)^(2)-2(x^(2)-9x)-80 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)-9x)^(2)-2(x^(2)-9x)-80 Answer:

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Define New Variable: Let's denote the expression inside the parentheses as a new variable to simplify the problem. Let u = x^2 - 9x. The expression becomes: (u)^2 - 2u - 80Factor Quadratic Expression: Now we have a quadratic in terms of u. We can factor this quadratic expression as we would normally do with any quadratic. We are looking for two numbers that multiply to -80 and add up to -2. These numbers are -10 and 8. So we can write: (u - 10)(u + 8)Substitute Back and Simplify: Now we substitute back x^2 - 9x for u to get the expression in terms of x: (x^2 - 9x - 10)(x^2 - 9x + 8)Factor First Quadratic: Next, we need to factor each quadratic expression. Starting with x^2 - 9x - 10, we look for two numbers that multiply to -10 and add up to -9. These numbers are -10 and 1. So we can write: (x - 10)(x + 1)Factor Second Quadratic: Now, we factor x^2 - 9x + 8. We look for two numbers that multiply to 8 and add up to -9. These numbers are -1 and -8. So we can write: (x - 1)(x - 8)Write Original Expression: Finally, we write the original expression as a product of four linear factors: (x - 10)(x + 1)(x - 1)(x - 8)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}-9 x\right)^{2}-2\left(x^{2}-9 x\right)-80$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2−9x)2−2(x2−9x)−80 \left(x^{2}-9 x\right)^{2}-2\left(x^{2}-9 x\right)-80 (x2−9x)2−2(x2−9x)−80\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}-9 x\right)^{2}-2\left(x^{2}-9 x\right)-80$ $\newline$ Answer: