Rewrite the expression as a product of four linear factors: (6x^(2)-x)^(2)-6(6x^(2)-x)+5 Answer:

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Rewrite the expression as a product of four linear factors:  (6x^(2)-x)^(2)-6(6x^(2)-x)+5 Answer:

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Identify Given Expression: Let's identify the given expression and look for a pattern that resembles a known algebraic identity. The given expression is: (6x^2 - x)^2 - 6(6x^2 - x) + 5 This expression resembles the form of a squared binomial minus the product of its square root and a constant, plus another constant. This pattern suggests that we might be dealing with a perfect square trinomial.Confirm Perfect Square Trinomial: To confirm if we have a perfect square trinomial, we need to find the square root of the first term and the last term and see if twice the product of the square roots equals the middle term. The square root of the first term (6x^2 - x)^2 is (6x^2 - x), and the square root of the last term 5 is √5. Now we check if 2 * (6x^2 - x) * √5 equals the middle term -6(6x^2 - x). 2 * (6x^2 - x) * √5 = 2 * √5 * 6x^2 - 2 * √5 * x This does not equal -6(6x^2 - x), so our expression is not a perfect square trinomial.Factor by Grouping: Since the expression is not a perfect square trinomial, we need to find another way to factor it. Let's try to factor by grouping. We rewrite the expression as a quadratic in terms of (6x^2 - x): Let y = (6x^2 - x), then the expression becomes: y^2 - 6y + 5 Now we factor this quadratic equation.Factor Quadratic Equation: We look for two numbers that multiply to 5 and add up to -6. These numbers are -5 and -1. So we can factor the quadratic as: (y - 5)(y - 1)Factor First Quadratic: Now we substitute back (6x^2 - x) for y: ((6x^2 - x) - 5)((6x^2 - x) - 1) This gives us: (6x^2 - x - 5)(6x^2 - x - 1)Factor Second Quadratic: Now we need to factor each quadratic separately. First, let's factor 6x^2 - x - 5. We look for two numbers that multiply to -30 (6 * -5) and add up to -1. These numbers are -6 and 5. So we can factor the quadratic as: (2x - 5)(3x + 1)Final Expression as Product: Next, we factor 6x^2 - x - 1. We look for two numbers that multiply to -6 (6 * -1) and add up to -1. These numbers are -3 and 2. So we can factor the quadratic as: (2x - 1)(3x + 1)Now we have the expression as a product of four linear factors: (2x - 5)(3x + 1)(2x - 1)(3x + 1)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(6 x^{2}-x\right)^{2}-6\left(6 x^{2}-x\right)+5$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(6x2−x)2−6(6x2−x)+5 \left(6 x^{2}-x\right)^{2}-6\left(6 x^{2}-x\right)+5 (6x2−x)2−6(6x2−x)+5\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(6 x^{2}-x\right)^{2}-6\left(6 x^{2}-x\right)+5$ $\newline$ Answer: