Factor Completelyminus, 10, h, squared, plus, 82, h, minus, 16−10h 2 +82h−16
Question
Factor Completelyminus, 10, h, squared, plus, 82, h, minus, 16−10h 2 +82h−16
Solution
The expression you provided seems to be a bit unclear, but if you're asking to factor the quadratic equation -10h^2 + 82h - 16, here are the steps:
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First, we can factor out a common factor of -2 from all terms to simplify the equation:
-2(5h^2 - 41h + 8)
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Now, we need to factor the quadratic 5h^2 - 41h + 8. We're looking for two numbers that multiply to (5*8 = 40) and add up to -41. Those numbers are -5 and -8.
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We rewrite -41h as -5h - 36h and factor by grouping:
-2[(5h^2 - 5h) - (36h - 8)]
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Factor out common factors from each group:
-2[h(5h - 1) - 8(5h - 1)]
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Now you can see that (5h - 1) is a common factor:
-2(5h - 1)(h - 8)
So, the factored form of -10h^2 + 82h - 16 is -2(5h - 1)(h - 8).
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