How do you factor #3x^2 + 54x + 243#?

1 Answer
Jun 14, 2015

Answer:

#3x^2+54x+243 = 3(x^2+18x+81) = 3(x+9)^2#

Explanation:

First separate the common scalar factor:

#3x^2+54x+243 = 3(x^2+18x+81)#

The remaining quadratic factor is recognisable as a perfect square trinomial in that it is of the form #a^2+2ab+b^2 = (a+b)^2# with #a=x# and #b=9#.

Hence:

#3(x^2+18x+81) = 3(x+9)^2#