Rewrite the expression as a product of four linear factors: (8x^(2)+9x)^(2)-13(8x^(2)+9x)-14 Answer:

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Rewrite the expression as a product of four linear factors:  (8x^(2)+9x)^(2)-13(8x^(2)+9x)-14 Answer:

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Recognize Quadratic Form: Recognize the given expression as a quadratic in form. The expression (8x^(2)+9x)^(2)-13(8x^(2)+9x)-14 resembles a quadratic equation in the form of (ax^2 + bx + c), where the variable x is replaced by (8x^2 + 9x).Substitute and Simplify: Let y = (8x^2 + 9x). Substitute y for (8x^2 + 9x) to simplify the expression. We get y^2 - 13y - 14.Factor Quadratic Equation: Factor the quadratic equation y^2 - 13y - 14. We look for two numbers that multiply to -14 and add up to -13. These numbers are -14 and 1. So, y^2 - 13y - 14 = (y - 14)(y + 1).Substitute Back and Expand: Substitute back (8x^2 + 9x) for y. Replace y with (8x^2 + 9x) in the factored form. We get (8x^2 + 9x - 14)(8x^2 + 9x + 1).Factor Further: Factor each quadratic expression further. We need to factor (8x^2 + 9x - 14) and (8x^2 + 9x + 1) into two linear factors each.Factor 8x^2 + 9x - 14: Factor 8x^2 + 9x - 14. We look for two numbers that multiply to 8*(-14) = -112 and add up to 9. These numbers are 16 and -7. We can write 9x as 16x - 7x, so the expression becomes 8x^2 + 16x - 7x - 14. Now, factor by grouping: (8x^2 + 16x) - (7x + 14) = 8x(x + 2) - 7(x + 2). Finally, we get (8x - 7)(x + 2).Factor 8x^2 + 9x + 1: Factor 8x^2 + 9x + 1. This expression is a bit trickier because the factors of 8 and 1 are not as straightforward. However, we can still attempt to factor by trial and error or by using the quadratic formula. Upon inspection, it seems that this expression does not factor nicely into linear factors with integer coefficients. This is a math error because we assumed it could be factored into linear factors, but it cannot.

Rewrite the expression as a product of four linear factors: $\newline$ $\left(8 x^{2}+9 x\right)^{2}-13\left(8 x^{2}+9 x\right)-14$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(8x2+9x)2−13(8x2+9x)−14 \left(8 x^{2}+9 x\right)^{2}-13\left(8 x^{2}+9 x\right)-14 (8x2+9x)2−13(8x2+9x)−14\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(8 x^{2}+9 x\right)^{2}-13\left(8 x^{2}+9 x\right)-14$ $\newline$ Answer: