Rewrite the expression as a product of four linear factors: (4x^(2)+x)^(2)-19(4x^(2)+x)+70 Answer:

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Rewrite the expression as a product of four linear factors:  (4x^(2)+x)^(2)-19(4x^(2)+x)+70 Answer:

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Identify Expression: Let's identify the expression we need to factor: (4x^2 + x)^2 - 19(4x^2 + x) + 70. This is a quadratic in form, with the ＂variable＂ being (4x^2 + x). Let's set u = 4x^2 + x to simplify the expression.Substitute Variable: Substitute u into the expression to see the quadratic form more clearly: u^2 - 19u + 70.Factor Quadratic Expression: Now we need to factor the quadratic expression u^2 - 19u + 70. We are looking for two numbers that multiply to 70 and add up to -19. These numbers are -14 and -5 because (-14) * (-5) = 70 and (-14) + (-5) = -19.Write Factored Form: We can now write the factored form of the quadratic as (u - 14)(u - 5).Substitute Back for u: Substitute back 4x^2 + x for u to get the factored form in terms of x: (4x^2 + x - 14)(4x^2 + x - 5).Factor Quadratic Expression Further: Now we need to factor each quadratic expression further. Let's start with 4x^2 + x - 14. We are looking for two numbers that multiply to -56 (4 * -14) and add up to 1. These numbers are 8 and -7 because (8) * (-7) = -56 and 8 + (-7) = 1.Write Factored Form: We can now write the factored form of 4x^2 + x - 14 as (4x - 7)(x + 2).Factor Quadratic Expression Further: Next, we factor 4x^2 + x - 5. We are looking for two numbers that multiply to -20 (4 * -5) and add up to 1. These numbers are 5 and -4 because (5) * (-4) = -20 and 5 + (-4) = 1.Write Factored Form: We can now write the factored form of 4x^2 + x - 5 as (4x - 5)(x + 1).Combine Linear Factors: Finally, we combine all the linear factors to express the original expression as a product of four linear factors: (4x - 7)(x + 2)(4x - 5)(x + 1).

Rewrite the expression as a product of four linear factors: $\newline$ $\left(4 x^{2}+x\right)^{2}-19\left(4 x^{2}+x\right)+70$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(4x2+x)2−19(4x2+x)+70 \left(4 x^{2}+x\right)^{2}-19\left(4 x^{2}+x\right)+70 (4x2+x)2−19(4x2+x)+70\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(4 x^{2}+x\right)^{2}-19\left(4 x^{2}+x\right)+70$ $\newline$ Answer: