Rewrite the expression as a product of four linear factors: (6x^(2)-11 x)^(2)-12(6x^(2)-11 x)-85 Answer:

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Rewrite the expression as a product of four linear factors:  (6x^(2)-11 x)^(2)-12(6x^(2)-11 x)-85 Answer:

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Identify and Recognize Quadratic Form: Identify the given expression and recognize that it resembles a quadratic in form, where the variable part is (6x^2 - 11x) instead of a simple x. The expression is a quadratic in (6x^2 - 11x): (6x^2 - 11x)^2 - 12(6x^2 - 11x) - 85Set Substitution for Simplification: Let's set a substitution to simplify the expression. Let u = 6x^2 - 11x. The expression then becomes: u^2 - 12u - 85 This is a quadratic equation in terms of u.Factor Quadratic Equation: Factor the quadratic equation u^2 - 12u - 85. We need to find two numbers that multiply to -85 and add up to -12. These numbers are -17 and 5. (u - 17)(u + 5) = 0Substitute Back and Factor in Terms of x: Now, substitute back 6x^2 - 11x for u to get the factors in terms of x: (6x^2 - 11x - 17)(6x^2 - 11x + 5) = 0Factor First Quadratic: Each of these quadratic factors can be further factored into linear factors. We will start with the first one: 6x^2 - 11x - 17. To factor this, we need to find two numbers that multiply to 6 * -17 = -102 and add up to -11. These numbers are -17 and 6. (3x - 17)(2x + 1) = 6x^2 - 11x - 17Factor Second Quadratic: Now, factor the second quadratic: 6x^2 - 11x + 5. We need to find two numbers that multiply to 6 * 5 = 30 and add up to -11. These numbers are -6 and -5. (3x - 5)(2x - 1) = 6x^2 - 11x + 5Combine Linear Factors: Combine all the linear factors to express the original expression as a product of four linear factors: (3x - 17)(2x + 1)(3x - 5)(2x - 1)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(6 x^{2}-11 x\right)^{2}-12\left(6 x^{2}-11 x\right)-85$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(6x2−11x)2−12(6x2−11x)−85 \left(6 x^{2}-11 x\right)^{2}-12\left(6 x^{2}-11 x\right)-85 (6x2−11x)2−12(6x2−11x)−85\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(6 x^{2}-11 x\right)^{2}-12\left(6 x^{2}-11 x\right)-85$ $\newline$ Answer: