Is it possible to factor #y= 4x^2 -12x + 9 #? If so, what are the factors?

1 Answer
Jan 15, 2016

Answer:

Yes. #y=(2x-3)^2#

Explanation:

If the general form of the factored quadratic is #y = (ax +b)(cx+d)# then
#y = acx^2 + (bc+ad)x +bd)#

This means that we need factors #a# and #c# that multiply to give #4# and #b# and #d# that multiply to give #9#.
#bc # and #ad# must add up to give # -12#

Because the sign of the middle term is negative and the sign of the last term is positive, both #b# and #d# must be negative.
In this example #ac# and #bd# both give squares - #4# and #9# respectively.
The answer is therefore #(2x - 3)(2x -3)#
#=(2x-3)^2#