Rewrite the expression as a product of four linear factors: (x^(2)+5x)^(2)-20(x^(2)+5x)+84 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)+5x)^(2)-20(x^(2)+5x)+84 Answer:

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Recognize Quadratic Form: Let's first recognize that the given expression is a quadratic in form, where the variable is not just x, but (x^2 + 5x). We can rewrite the expression as a quadratic equation: Let u = x^2 + 5x. Then the expression becomes: u^2 - 20u + 84Factor Quadratic Expression: Now, we need to factor the quadratic expression u^2 - 20u + 84. To do this, we look for two numbers that multiply to 84 and add up to -20. These numbers are -14 and -6. So we can write the factored form as: (u - 14)(u - 6)Substitute Back and Simplify: Next, we substitute back x^2 + 5x for u in each factor to get the expression in terms of x: (x^2 + 5x - 14)(x^2 + 5x - 6)Factor First Quadratic Expression: Now, we need to factor each quadratic expression further. Starting with x^2 + 5x - 14, we look for two numbers that multiply to -14 and add up to 5. These numbers are 7 and -2. So we can write the factored form as: (x + 7)(x - 2)Factor Second Quadratic Expression: Next, we factor the second quadratic expression x^2 + 5x - 6. We look for two numbers that multiply to -6 and add up to 5. These numbers are 6 and -1. So we can write the factored form as: (x + 6)(x - 1)Combine Linear Factors: Finally, we combine all the linear factors to express the original expression as a product of four linear factors: (x + 7)(x - 2)(x + 6)(x - 1)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+5 x\right)^{2}-20\left(x^{2}+5 x\right)+84$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2+5x)2−20(x2+5x)+84 \left(x^{2}+5 x\right)^{2}-20\left(x^{2}+5 x\right)+84 (x2+5x)2−20(x2+5x)+84\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+5 x\right)^{2}-20\left(x^{2}+5 x\right)+84$ $\newline$ Answer: