Rewrite the expression as a product of four linear factors: (x^(2)+3x)^(2)-16(x^(2)+3x)-36 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)+3x)^(2)-16(x^(2)+3x)-36 Answer:

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Identify Expression: Let's first identify the expression we need to factor: Expression: (x^2 + 3x)^2 - 16(x^2 + 3x) - 36 We notice that this is a quadratic in form, where the variable part (x^2 + 3x) is squared and appears linearly as well. We can use a substitution method to simplify the factoring process. Let u = x^2 + 3x. Then our expression becomes: u^2 - 16u - 36Factor Quadratic Expression: Now we need to factor the quadratic expression u^2 - 16u - 36. This is a standard quadratic factoring problem. We look for two numbers that multiply to -36 and add up to -16. These numbers are -18 and +2. So we can write the quadratic as: (u - 18)(u + 2)Substitute and Simplify: Next, we substitute back x^2 + 3x for u to get the expression in terms of x: (x^2 + 3x - 18)(x^2 + 3x + 2) Now we need to factor each of these quadratic expressions further.Factor First Quadratic: We start with the first quadratic expression x^2 + 3x - 18. We need to find two numbers that multiply to -18 and add up to 3. These numbers are 6 and -3. So we can write the quadratic as: (x + 6)(x - 3)Factor Second Quadratic: Now we factor the second quadratic expression x^2 + 3x + 2. We need to find two numbers that multiply to 2 and add up to 3. These numbers are 2 and 1. So we can write the quadratic as: (x + 2)(x + 1)Combine Factors: Finally, we write the original expression as a product of four linear factors by combining the factors we found: (x + 6)(x - 3)(x + 2)(x + 1) This is the expression rewritten as a product of four linear factors.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+3 x\right)^{2}-16\left(x^{2}+3 x\right)-36$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2+3x)2−16(x2+3x)−36 \left(x^{2}+3 x\right)^{2}-16\left(x^{2}+3 x\right)-36 (x2+3x)2−16(x2+3x)−36\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+3 x\right)^{2}-16\left(x^{2}+3 x\right)-36$ $\newline$ Answer: