Rewrite the expression as a product of four linear factors: (x^(2)+5x)^(2)-2(x^(2)+5x)-24 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)+5x)^(2)-2(x^(2)+5x)-24 Answer:

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Identify Expression: Let's first identify the expression we need to factor: Expression: (x^2 + 5x)^2 - 2(x^2 + 5x) - 24 We notice that this is a quadratic in form, where the variable part (x^2 + 5x) is squared. Let's set a substitution to simplify the expression. Let u = x^2 + 5x. Now our expression becomes: u^2 - 2u - 24Set Substitution: Next, we factor the quadratic expression u^2 - 2u - 24 as if it were a regular quadratic equation. We look for two numbers that multiply to -24 and add up to -2. These numbers are -6 and +4. So we can write the factored form as: (u - 6)(u + 4)Factor Quadratic Expression: Now we substitute back x^2 + 5x for u to get the expression in terms of x: (x^2 + 5x - 6)(x^2 + 5x + 4)Substitute Back to x: We now need to factor each quadratic expression further to get the linear factors. Let's start with the first 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)Factor First Quadratic: Now let's factor the second quadratic expression: x^2 + 5x + 4 We look for two numbers that multiply to 4 and add up to 5. These numbers are +4 and +1. So we can write the factored form as: (x + 4)(x + 1)Factor Second Quadratic: Finally, we combine all the linear factors to express the original expression as a product of four linear factors: (x + 6)(x - 1)(x + 4)(x + 1)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+5 x\right)^{2}-2\left(x^{2}+5 x\right)-24$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2+5x)2−2(x2+5x)−24 \left(x^{2}+5 x\right)^{2}-2\left(x^{2}+5 x\right)-24 (x2+5x)2−2(x2+5x)−24\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+5 x\right)^{2}-2\left(x^{2}+5 x\right)-24$ $\newline$ Answer: