Rewrite the expression as a product of four linear factors: (7x^(2)-10 x)^(2)-14(7x^(2)-10 x)-51 Answer:

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Rewrite the expression as a product of four linear factors:  (7x^(2)-10 x)^(2)-14(7x^(2)-10 x)-51 Answer:

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Identify Expression and Form: Identify the given expression and recognize that it resembles a quadratic in form, where the variable part is (7x^2 - 10x). The expression is: (7x^2 - 10x)^2 - 14(7x^2 - 10x) - 51 Let's set u = 7x^2 - 10x, so the expression becomes a quadratic in u: u^2 - 14u - 51Set Variable and Simplify: Factor the quadratic expression u^2 - 14u - 51. We are looking for two numbers that multiply to -51 and add up to -14. The numbers that satisfy these conditions are -17 and 3, since (-17) * 3 = -51 and (-17) + 3 = -14. So we can factor the quadratic as (u - 17)(u + 3).Factor Quadratic Expression: Now, substitute back 7x^2 - 10x for u in the factored form. We get (7x^2 - 10x - 17)(7x^2 - 10x + 3).Substitute and Expand: Next, we need to factor each of these quadratic expressions further to find the linear factors. Starting with 7x^2 - 10x - 17, we look for two numbers that multiply to 7 * -17 = -119 and add up to -10. The numbers that satisfy these conditions are -17 and 7, since (-17) * 7 = -119 and (-17) + 7 = -10. So we can factor the quadratic as (7x + 7)(x - 17).Factor First Quadratic: Now, factor the second quadratic expression 7x^2 - 10x + 3. We look for two numbers that multiply to 7 * 3 = 21 and add up to -10. The numbers that satisfy these conditions are -7 and -3, since (-7) * (-3) = 21 and (-7) + (-3) = -10. However, upon checking the multiplication, we find that -7 and -3 do not multiply to 21. This is a math error.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(7 x^{2}-10 x\right)^{2}-14\left(7 x^{2}-10 x\right)-51$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(7x2−10x)2−14(7x2−10x)−51 \left(7 x^{2}-10 x\right)^{2}-14\left(7 x^{2}-10 x\right)-51 (7x2−10x)2−14(7x2−10x)−51\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(7 x^{2}-10 x\right)^{2}-14\left(7 x^{2}-10 x\right)-51$ $\newline$ Answer: