How do you factor #12x²-24x+9#?

1 Answer
Nov 3, 2016

Answer:

#12x^2-24x+9 = 3(2x-1)(2x-3)#

Explanation:

First separate out the common scalar factor #3#:

#12x^2-24x+9 = 3(4x^2-8x+3)#

To factor the remaining quadratic #4x^2-8x+3# use an AC method:

Find a pair of factors of #AC = 4*3=12# with sum #B=8#

The pair #6, 2# works.

Use this pair to split the middle term and factor by grouping:

#4x^2-8x+3 = 4x^2-6x-2x+3#

#color(white)(4x^2-8x+3) = (4x^2-6x)-(2x-3)#

#color(white)(4x^2-8x+3) = 2x(2x-3)-1(2x-3)#

#color(white)(4x^2-8x+3) = (2x-1)(2x-3)#

Putting it all together:

#12x^2-24x+9 = 3(2x-1)(2x-3)#