How do you factor # 27x^3 + 54 x^2 + 36x +8# by grouping?

1 Answer
Jun 19, 2016

Answer:

Note that the first and last terms are perfect cubes and find:

#27x^3+54x^2+36x+8 = (3x+2)^3#

Explanation:

Notice that the ratio between the first and second coefficients is not the same as that between the third and fourth.

That is: #27/54 != 36/8#

So this does not factor by grouping.

#color(white)#
Note that the first and last terms are both perfect cubes:

#27x^3 = (3x)^3#

#8 = 2^3#

So we might try #(3x+2)^3#:

#(3x+2)^3 = 27x^3+54x^2+36x+8#

Yes - that's our factoring.