Question

Factor −20x² + x + 12.

Answer 1

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)