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

1 Answer
Oct 30, 2016

Answer:

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

Explanation:

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#