Rewrite the expression as a product of four linear factors: (x^(2)-x)^(2)-22(x^(2)-x)+40 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)-x)^(2)-22(x^(2)-x)+40 Answer:

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Identify Structure: Let's first identify the structure of the given expression and see if it resembles any known algebraic identities. The expression is:  (x^2 - x)^2 - 22(x^2 - x) + 40  This looks like a quadratic equation in the form of (a^2 - 2ab + b^2), where 'a' is (x^2 - x) and 'b' is some number we need to find. To factor it, we will consider it as a quadratic in terms of (x^2 - x).Substitute and Simplify: Let's denote u = x^2 - x. Then the expression becomes:  u^2 - 22u + 40  Now we need to factor this quadratic expression.Factor Quadratic Expression: To factor the quadratic expression u^2 - 22u + 40, we need to find two numbers that multiply to 40 and add up to -22. These numbers are -20 and -2 because (-20) * (-2) = 40 and (-20) + (-2) = -22.  So we can write the quadratic as:  (u - 20)(u - 2)Factor First Quadratic: Now we substitute back x^2 - x for u in the factored form to get:  (x^2 - x - 20)(x^2 - x - 2)  Now we need to factor each of these quadratic expressions further.Factor Second Quadratic: We will factor the first quadratic expression x^2 - x - 20. We need to find two numbers that multiply to -20 and add up to -1 (the coefficient of x). These numbers are -5 and 4 because (-5) * 4 = -20 and (-5) + 4 = -1.  So we can write the first quadratic as:  (x - 5)(x + 4)Final Linear Factors: Next, we will factor the second quadratic expression x^2 - x - 2. We need to find two numbers that multiply to -2 and add up to -1 (the coefficient of x). These numbers are -2 and 1 because (-2) * 1 = -2 and (-2) + 1 = -1.  So we can write the second quadratic as:  (x - 2)(x + 1)Now we have factored the original expression into four linear factors:  (x - 5)(x + 4)(x - 2)(x + 1)  This is the product of four linear factors for the given expression.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}-x\right)^{2}-22\left(x^{2}-x\right)+40$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2−x)2−22(x2−x)+40 \left(x^{2}-x\right)^{2}-22\left(x^{2}-x\right)+40 (x2−x)2−22(x2−x)+40\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}-x\right)^{2}-22\left(x^{2}-x\right)+40$ $\newline$ Answer: