How do you factor #12x^2 + 60x + 75#?

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Answer 1 · 2016-10-30T00:08:54

#12x^2+60x+75 = 3(2x+5)^2#

Note that all of the terms are divisible by #3#, so separate that out as a scalar factor first:

#12x^2+60x+75 = 3(4x^2+20x+25)#

Next note that #4x^2 = (2x)^2# and #25 = 5^2# are both perfect squares. So do we have a perfect square trinomial?

Let's try:

#(2x+5)^2 = (2x)^2+2(2x)(5) + 5^2 = 4x^2+20x+25#

...matching our parenthesised quadratic.

So putting it all together we have:

#12x^2+60x+75 = 3(2x+5)^2#