Rewrite the expression as a product of four linear factors: (3x^(2)-10 x)^(2)-10(3x^(2)-10 x)-39 Answer:

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Rewrite the expression as a product of four linear factors:  (3x^(2)-10 x)^(2)-10(3x^(2)-10 x)-39 Answer:

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Identify Expression: Identify the given expression and recognize that it resembles a quadratic in form, where the variable part is (3x^2 - 10x). The expression is: (3x^2 - 10x)^2 - 10(3x^2 - 10x) - 39 Let's denote u = 3x^2 - 10x, so the expression becomes: u^2 - 10u - 39Factor Quadratic: Factor the quadratic expression u^2 - 10u - 39. We are looking for two numbers that multiply to -39 and add up to -10. The numbers that satisfy these conditions are -13 and +3. So we can write the quadratic as: (u - 13)(u + 3)Substitute and Simplify: Now, substitute back the original expression for u, which is 3x^2 - 10x, into the factored form: (3x^2 - 10x - 13)(3x^2 - 10x + 3)Factor First Quadratic: Notice that each quadratic factor can be further factored into two linear factors. We will start with the first quadratic factor: 3x^2 - 10x - 13 To factor this, we need to find two numbers that multiply to 3*(-13) = -39 and add up to -10. These numbers are the same as before, -13 and +3, but we need to consider the coefficient of x^2, which is 3. We can write the factorization as: (3x + 1)(x - 13)Factor Second Quadratic: Now, factor the second quadratic factor: 3x^2 - 10x + 3 Again, we need to find two numbers that multiply to 3*3 = 9 and add up to -10. These numbers are -9 and -1. We can write the factorization as: (3x - 1)(x - 3)Combine Linear Factors: Combine all the linear factors to express the original expression as a product of four linear factors: (3x + 1)(x - 13)(3x - 1)(x - 3)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(3 x^{2}-10 x\right)^{2}-10\left(3 x^{2}-10 x\right)-39$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(3x2−10x)2−10(3x2−10x)−39 \left(3 x^{2}-10 x\right)^{2}-10\left(3 x^{2}-10 x\right)-39 (3x2−10x)2−10(3x2−10x)−39\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(3 x^{2}-10 x\right)^{2}-10\left(3 x^{2}-10 x\right)-39$ $\newline$ Answer: