Factor −20x² + x + 12.

Question

03-06-2018
Mathematics

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Factor −20x² + x + 12.

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Аноним Аноним · Answer 1 · 2018-06-03T22:13:04+02:00

The answer is -(5x-4)(4x+3)

Factor out a negative from the entire expression

−20x² + x + 12
= −(20x² - x - 12)

Find two numbers so that they

⇒ Multiply to get 20 * -12 = -240
⇒ and add to get -1 (coefficient on x term)

These two numbers are -16 and 15 (not very obvious; might have to crunch some numbers)

We can break down the x term using -16 and 15 as coefficients on x

−(20x² - x - 12)
= −(20x² - 16x + 15x - 12)

We factor by grouping. Factor 4x out of 20x² - 16x and 3 out of 15x - 12 to get

= −[ 4x(5x - 4) + 3(5x - 4) ]

Factor out (5x-4) to get

= -(5x-4)[4x + 3]
= -(5x-4)(4x+3)