How do you factor a perfect square trinomial #9x^2 − 12x + 4#?

1 Answer
Jul 7, 2015

Answer:

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

Explanation:

If #Ax^2+Bx+C = (ax+c)^2# is a perfect square trinomial
then for some set #{a,c}#
#color(white)("XXXX")##A=a^2#
#color(white)("XXXX")##C=c^2#
and
#color(white)("XXXX")##B = 2ac#

Given that #9x^2-12x+4# is a perfect square trinomial
#color(white)("XXXX")##A=9x^2 rarr a=3x#
#color(white)("XXXX")##C=4 rarr c=+-2#

Since #B=-12x = 2ac = 2(3x)c#
#color(white)("XXXX")##rarr c=-2#