Rewrite the expression as a product of four linear factors: (5x^(2)-14 x)^(2)-22(5x^(2)-14 x)+57 Answer:

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Rewrite the expression as a product of four linear factors:  (5x^(2)-14 x)^(2)-22(5x^(2)-14 x)+57 Answer:

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Identify and Recognize Form: Identify the given expression and recognize that it resembles a quadratic in form, where the variable part is (5x^2 - 14x). The expression is: (5x^2 - 14x)^2 - 22(5x^2 - 14x) + 57Substitution for Simplification: Let u = 5x^2 - 14x. This substitution will simplify the expression into a quadratic form. The expression becomes: u^2 - 22u + 57Factor Quadratic Expression: Factor the quadratic expression u^2 - 22u + 57. We need to find two numbers that multiply to 57 and add up to -22. The numbers that satisfy these conditions are -19 and -3, since (-19) * (-3) = 57 and (-19) + (-3) = -22.Write Factored Form: Write the factored form of the quadratic using the numbers found in the previous step. The factored form is: (u - 19)(u - 3)Substitute Back for u: Substitute back 5x^2 - 14x for u in the factored expression. The expression becomes: (5x^2 - 14x - 19)(5x^2 - 14x - 3)Further Factor Quadratics: Now, factor each quadratic expression further to find the linear factors. Starting with 5x^2 - 14x - 19, we look for two numbers that multiply to 5*(-19) = -95 and add up to -14. The numbers that satisfy these conditions are -19 and 5, since (-19) * 5 = -95 and (-19) + 5 = -14. However, these numbers do not work in this context because they do not allow us to factor the quadratic into two linear factors with integer coefficients. We need to find another approach to factor this quadratic.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(5 x^{2}-14 x\right)^{2}-22\left(5 x^{2}-14 x\right)+57$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(5x2−14x)2−22(5x2−14x)+57 \left(5 x^{2}-14 x\right)^{2}-22\left(5 x^{2}-14 x\right)+57 (5x2−14x)2−22(5x2−14x)+57\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(5 x^{2}-14 x\right)^{2}-22\left(5 x^{2}-14 x\right)+57$ $\newline$ Answer: