Rewrite the expression as a product of four linear factors: (x^(2)+7x)^(2)+4(x^(2)+7x)-96 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)+7x)^(2)+4(x^(2)+7x)-96 Answer:

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Recognize Structure: Recognize the structure of the given expression The given expression resembles a quadratic in form, where the variable part (x^2 + 7x) is squared and then linearly combined with a constant. This suggests that we might be able to factor it by treating (x^2 + 7x) as a single variable.Substitute Single Variable: Substitute a single variable for the repeated expression Let y = x^2 + 7x. The expression becomes y^2 + 4y - 96.Factor Quadratic Expression: Factor the quadratic expression in terms of y We need to find two numbers that multiply to -96 and add to 4. These numbers are 12 and -8. So, y^2 + 4y - 96 = (y + 12)(y - 8).Substitute Back: Substitute back x^2 + 7x for y Replace y with x^2 + 7x in the factored form to get: (x^2 + 7x + 12)(x^2 + 7x - 8).Factor Each Quadratic: Factor each quadratic separately We now have two quadratics to factor. We need to find two numbers that multiply to 12 and add to 7 for the first quadratic, and two numbers that multiply to -8 and add to 7 for the second quadratic.  For the first quadratic: The numbers are 3 and 4. So, x^2 + 7x + 12 = (x + 3)(x + 4).  For the second quadratic: The numbers are 1 and -8. So, x^2 + 7x - 8 = (x + 8)(x - 1).Combine Factors: Combine the factors to express the original expression as a product of four linear factors The original expression is now factored as: (x + 3)(x + 4)(x + 8)(x - 1).

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+7 x\right)^{2}+4\left(x^{2}+7 x\right)-96$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2+7x)2+4(x2+7x)−96 \left(x^{2}+7 x\right)^{2}+4\left(x^{2}+7 x\right)-96 (x2+7x)2+4(x2+7x)−96\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+7 x\right)^{2}+4\left(x^{2}+7 x\right)-96$ $\newline$ Answer: