Rewrite the expression as a product of four linear factors: (5x^(2)-12 x)^(2)-2(5x^(2)-12 x)-63 Answer:

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Rewrite the expression as a product of four linear factors:  (5x^(2)-12 x)^(2)-2(5x^(2)-12 x)-63 Answer:

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Write Given Expression: Let's first write down the given expression: (5x^2 - 12x)^2 - 2(5x^2 - 12x) - 63 We will try to recognize this as a quadratic in form of (ax^2 + bx + c) where x is replaced by (5x^2 - 12x).Recognize Quadratic Form: To factor the quadratic, we look for two numbers that multiply to ac (where a is the coefficient of the squared term and c is the constant term) and add to b (the coefficient of the linear term). In this case, a = 1, b = -2, and c = -63. ac = 1 * -63 = -63 We need two numbers that multiply to -63 and add to -2.Factor Quadratic: The two numbers that satisfy these conditions are -9 and +7 because -9 * 7 = -63 and -9 + 7 = -2. Now we can rewrite the quadratic as: (5x^2 - 12x - 9)(5x^2 - 12x + 7)Find Two Numbers: Next, we need to factor each quadratic factor further into two linear factors. We start with the first quadratic factor: 5x^2 - 12x - 9 We look for two numbers that multiply to 5 * -9 = -45 and add to -12.Rewrite Quadratic: The two numbers that satisfy these conditions are -15 and +3 because -15 * 3 = -45 and -15 + 3 = -12. We can now factor the first quadratic factor as: (5x - 15)(x + 3)Factor First Quadratic: Now we factor the second quadratic factor: 5x^2 - 12x + 7 We look for two numbers that multiply to 5 * 7 = 35 and add to -12.Factor Second Quadratic: The two numbers that satisfy these conditions are -5 and -7 because -5 * -7 = 35 and -5 - 7 = -12. We can now factor the second quadratic factor as: (5x - 7)(x - 1)Combine Linear Factors: Combining all the linear factors, we get the expression as a product of four linear factors: (5x - 15)(x + 3)(5x - 7)(x - 1)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(5 x^{2}-12 x\right)^{2}-2\left(5 x^{2}-12 x\right)-63$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(5x2−12x)2−2(5x2−12x)−63 \left(5 x^{2}-12 x\right)^{2}-2\left(5 x^{2}-12 x\right)-63 (5x2−12x)2−2(5x2−12x)−63\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(5 x^{2}-12 x\right)^{2}-2\left(5 x^{2}-12 x\right)-63$ $\newline$ Answer: