Rewrite the expression as a product of four linear factors: (2x^(2)-13 x)^(2)-(2x^(2)-13 x)-42 Answer:

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Rewrite the expression as a product of four linear factors:  (2x^(2)-13 x)^(2)-(2x^(2)-13 x)-42 Answer:

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Identify Expression: Let's first identify the expression we need to factor: (2x^2 - 13x)^2 - (2x^2 - 13x) - 42 Notice that this expression is a quadratic in form, where (2x^2 - 13x) is playing the role of a single variable. Let's substitute u = (2x^2 - 13x) to simplify the expression.Substitute and Simplify: Substitute u into the expression to get a quadratic in terms of u: u^2 - u - 42 Now, we need to factor this quadratic expression.Factor Quadratic Expression: To factor the quadratic expression u^2 - u - 42, we look for two numbers that multiply to -42 and add up to -1. These numbers are -7 and 6. So, we can write the quadratic as: (u - 7)(u + 6)Find Factors: Now, we need to substitute back (2x^2 - 13x) for u in each factor: (2x^2 - 13x - 7)(2x^2 - 13x + 6) Next, we need to factor each quadratic expression further.Substitute Back and Factor: Let's start with the first quadratic expression: 2x^2 - 13x - 7 We need to find two numbers that multiply to 2*(-7) = -14 and add up to -13. These numbers are -14 and 1. However, since the coefficient of x^2 is 2, we need to use the AC method or other factoring techniques to factor this expression. Let's check if it can be factored easily.Factor First Quadratic: Upon attempting to factor 2x^2 - 13x - 7, we find that it does not factor nicely into linear factors with integer coefficients. This means we have made a mistake, as the original problem asks for a product of four linear factors. We need to re-evaluate our approach to factoring the quadratic expressions.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(2 x^{2}-13 x\right)^{2}-\left(2 x^{2}-13 x\right)-42$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(2x2−13x)2−(2x2−13x)−42 \left(2 x^{2}-13 x\right)^{2}-\left(2 x^{2}-13 x\right)-42 (2x2−13x)2−(2x2−13x)−42\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(2 x^{2}-13 x\right)^{2}-\left(2 x^{2}-13 x\right)-42$ $\newline$ Answer: