Question

Factor by grouping. 12x^3−20x^2+3x-5

Answer 1

12x³ - 20x² + 3x - 5
4x²(3x) - 4x²(5) + 1(3x) - 1(5)
4x²(3x - 5) + 1(3x - 5)
(4x² + 1)(3x - 5)

Answer 2

First, group them in 2's (2 numbers per group)
and see which ones have the factors of each other

you want to group 12x^3 with 3x because 3 is a factor of 12
then you want to group -20x^2 and -5 together becuase 5 is a factor of 20 so
(12x^3+3x)+(-20x^2-5)
undistribute
(3x)(4x^2+1)+(-5)(4x^2+1)
revese distribute (ab+ac=a(b+c))
(3x-5)(4x^2+1)