Rewrite the expression as a product of four linear factors: (12x^(2)+5x)^(2)-9(12x^(2)+5x)+14 Answer:

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Rewrite the expression as a product of four linear factors:  (12x^(2)+5x)^(2)-9(12x^(2)+5x)+14 Answer:

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Recognize quadratic form: Recognize the given expression as a quadratic in form. The given expression is: (12x^(2)+5x)^(2)-9(12x^(2)+5x)+14 This is a quadratic equation in the form of (ax+b)^2 - c(ax+b) + d, where a = 12, b = 5, and c = 9, d = 14.Substitute variable y: Let y = 12x^2 + 5x. We can substitute y for 12x^2 + 5x to make the expression easier to work with. So the expression becomes: y^2 - 9y + 14Factor quadratic expression: Factor the quadratic expression. We need to factor y^2 - 9y + 14. To factor, we look for two numbers that multiply to 14 and add up to -9. The numbers that satisfy these conditions are -7 and -2. So we can write the quadratic as: (y - 7)(y - 2)Substitute back for y: Substitute back 12x^2 + 5x for y. Now we replace y with 12x^2 + 5x in the factored form: (12x^2 + 5x - 7)(12x^2 + 5x - 2)Factor each quadratic further: Factor each quadratic expression further. We need to factor each quadratic expression into two linear factors. Starting with 12x^2 + 5x - 7, we look for two numbers that multiply to -84 (12 * -7) and add up to 5. These numbers are 7 and -12. So we can write the quadratic as: (3x - 7)(4x + 1)  Similarly, for 12x^2 + 5x - 2, we look for two numbers that multiply to -24 (12 * -2) and add up to 5. These numbers are 6 and -4. So we can write the quadratic as: (3x - 2)(4x + 1)Combine linear factors: Combine the linear factors to express the original expression. Now we combine all the linear factors to express the original expression as a product of four linear factors: (3x - 7)(4x + 1)(3x - 2)(4x + 1)Check for repeated factors: Check for repeated factors. We notice that the factor (4x + 1) is repeated. So we can write the final expression as: (3x - 7)(4x + 1)^2(3x - 2)Verify full factorization: Verify that the expression is fully factored. We have expressed the original expression as a product of four linear factors, including the repeated factor. There are no further factors to extract, and the expression is fully factored.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(12 x^{2}+5 x\right)^{2}-9\left(12 x^{2}+5 x\right)+14$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(12x2+5x)2−9(12x2+5x)+14 \left(12 x^{2}+5 x\right)^{2}-9\left(12 x^{2}+5 x\right)+14 (12x2+5x)2−9(12x2+5x)+14\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(12 x^{2}+5 x\right)^{2}-9\left(12 x^{2}+5 x\right)+14$ $\newline$ Answer: