How do you know if #x^2 - 24x + 144# is a perfect square trinomial and how do you factor it?

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Answer 1 · 2015-06-09T07:06:48

Comparing with the form #a^2-2ab+b^2 = (a-b)^2#, we find #x^2-24x+144 = (x-12)^2#

All perfect square trinomials are of the form:

#a^2+-2ab+b^2 = (a+-b)^2#

In our case we see:

#x^2-24x+144#

#=x^2-24x+12^2#

#=x^2-(2*x*12)+12^2#

which is of the form #a^2-2ab+b^2# with #a=x# and #b=12#, so

#=(x-12)^2#