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: (x^2 - 3x)^2 - 16(x^2 - 3x) - 36. Notice that this is a quadratic in form, where the variable part is (x^2 - 3x). Let's set u = x^2 - 3x to simplify our expression.Set Simplification Variable: Now, rewrite the expression in terms of u: u^2 - 16u - 36. This is a quadratic equation that we can factor.Rewrite in Terms of u: To factor the quadratic equation u^2 - 16u - 36, we need to find two numbers that multiply to -36 and add up to -16. These numbers are -18 and +2.Factor Quadratic Equation: Now we can write the factored form of the quadratic equation: (u - 18)(u + 2).Write Factored Form: Next, we substitute back x^2 - 3x for u to get the factored form in terms of x: (x^2 - 3x - 18)(x^2 - 3x + 2).Factor x^2 - 3x - 18: We now need to factor each of these quadratic expressions further. Starting with x^2 - 3x - 18, we look for two numbers that multiply to -18 and add up to -3. These numbers are -6 and +3.Factor x^2 - 3x + 2: The factored form of x^2 - 3x - 18 is (x - 6)(x + 3).Combine Linear Factors: Now, we factor x^2 - 3x + 2. We look for two numbers that multiply to +2 and add up to -3. These numbers are -2 and -1.The factored form of x^2 - 3x + 2 is (x - 2)(x - 1).Finally, we combine all the linear factors to express the original expression as a product of four linear factors: (x - 6)(x + 3)(x - 2)(x - 1).

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: