Rewrite the expression as a product of four linear factors: (3x^(2)-7x)^(2)-16(3x^(2)-7x)+60 Answer:

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Rewrite the expression as a product of four linear factors:  (3x^(2)-7x)^(2)-16(3x^(2)-7x)+60 Answer:

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Identify Given Expression: Identify the given expression and recognize that it resembles a quadratic in form, where the variable part is (3x^2 - 7x). The expression is: (3x^2 - 7x)^2 - 16(3x^2 - 7x) + 60Transform to Quadratic Form: Notice that the expression can be considered as a quadratic equation in terms of (3x^2 - 7x). Let's denote u = 3x^2 - 7x. The expression becomes: u^2 - 16u + 60Factor Quadratic Expression: Factor the quadratic expression u^2 - 16u + 60. We are looking for two numbers that multiply to 60 and add up to -16. These numbers are -10 and -6. (u - 10)(u - 6) = u^2 - 16u + 60Substitute Back for u: Substitute back 3x^2 - 7x for u in the factored form. (3x^2 - 7x - 10)(3x^2 - 7x - 6)Factor First Quadratic Expression: Now, factor each quadratic expression further into two linear factors. We start with 3x^2 - 7x - 10. We need to find two numbers that multiply to (3 * -10) = -30 and add up to -7. These numbers are -10 and +3. (3x + 3)(x - 10)Factor Second Quadratic Expression: Next, factor the second quadratic expression 3x^2 - 7x - 6. We need to find two numbers that multiply to (3 * -6) = -18 and add up to -7. These numbers are -9 and +2. (3x + 2)(x - 3)Combine Linear Factors: Combine all the linear factors to express the original expression as a product of four linear factors. (3x + 3)(x - 10)(3x + 2)(x - 3)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(3 x^{2}-7 x\right)^{2}-16\left(3 x^{2}-7 x\right)+60$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(3x2−7x)2−16(3x2−7x)+60 \left(3 x^{2}-7 x\right)^{2}-16\left(3 x^{2}-7 x\right)+60 (3x2−7x)2−16(3x2−7x)+60\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(3 x^{2}-7 x\right)^{2}-16\left(3 x^{2}-7 x\right)+60$ $\newline$ Answer: