Rewrite the expression as a product of four linear factors: (6x^(2)+19 x)^(2)-8(6x^(2)+19 x)-33 Answer:

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Rewrite the expression as a product of four linear factors:  (6x^(2)+19 x)^(2)-8(6x^(2)+19 x)-33 Answer:

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Identify Expression: Let's first identify the expression we need to factor:  (6x^2 + 19x)^2 - 8(6x^2 + 19x) - 33 This is a quadratic in form, where the variable part (6x^2 + 19x) is squared. We can use a substitution to make it look like a standard quadratic equation. Let's let u = 6x^2 + 19x.Substitution with u: Now we rewrite the expression in terms of u: u^2 - 8u - 33 This is a quadratic equation that we can factor.Rewrite in terms of u: We need to find two numbers that multiply to -33 and add up to -8. These numbers are -11 and 3. So we can write the quadratic as: (u - 11)(u + 3)Factor quadratic: Now we substitute back 6x^2 + 19x for u to get: (6x^2 + 19x - 11)(6x^2 + 19x + 3)Substitute back for u: Each of these quadratic factors can be factored further. We start with the first one: 6x^2 + 19x - 11 We need to find two numbers that multiply to 6 * -11 = -66 and add up to 19. These numbers are 22 and -3. So we can write the quadratic as: (2x - 1)(3x + 11)Factor first quadratic: Now we factor the second quadratic: 6x^2 + 19x + 3 We need to find two numbers that multiply to 6 * 3 = 18 and add up to 19. These numbers are 18 and 1. So we can write the quadratic as: (x + 1)(6x + 3)Factor second quadratic: We can simplify the second factor further by taking out a common factor of 3: (x + 1)(3)(2x + 1)Combine all factors: Now we combine all the factors to express the original expression as a product of four linear factors: (2x - 1)(3x + 11)(x + 1)(2x + 1)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(6 x^{2}+19 x\right)^{2}-8\left(6 x^{2}+19 x\right)-33$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(6x2+19x)2−8(6x2+19x)−33 \left(6 x^{2}+19 x\right)^{2}-8\left(6 x^{2}+19 x\right)-33 (6x2+19x)2−8(6x2+19x)−33\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(6 x^{2}+19 x\right)^{2}-8\left(6 x^{2}+19 x\right)-33$ $\newline$ Answer: