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Solve each of the following using factoring. 50x^(3)+125x^(2)-18 x-45=0

Solve each of the following using factoring.\newline50x3+125x2−18x−45=050x^{3}+125x^{2}-18x-45=0

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Full solution

Q. Solve each of the following using factoring.\newline50x3+125x2−18x−45=050x^{3}+125x^{2}-18x-45=0
  1. Factor GCF from groups: Step 11: Factor out the greatest common factor (GCF) from each group.\newlineFirst, group the terms: (50x3+125x2)+(−18x−45)(50x^3 + 125x^2) + (-18x - 45).\newlineFactor out the GCF from each group:\newline50x2(x+2.5)−9(2x+5)50x^2(x + 2.5) - 9(2x + 5).
  2. Correct second group factorization: Step 22: Notice a mistake in the factorization of the second group.\newlineCorrect factorization should be:\newline50x2(x+2.5)−9(2x+5)50x^2(x + 2.5) - 9(2x + 5) is incorrect.\newlineCorrect to: 50x2(x+2.5)−9(2x+5)50x^2(x + 2.5) - 9(2x + 5).

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