How do you use the grouping method to factor #2x^3 + 12 x^2 + 5x + 30# completely?

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Answer 1 · 2018-04-17T13:45:44

#(x+6)(2x^2+5)#

#2x^3+12x^2+5x+30#

=#2x^2(x+6)+5(x+6)#

=#(x+6)(2x^2+5)#

Answer 2 · 2018-04-17T13:47:23

#(2x^2+5)(x+6)#

We have four terms, so we're going to make two groups of two terms as follows:

#(2x^3+12x^2)+(5x+30)#

Let's examine each group and see how we can factor it.

#2x^3+12x^2# has the greatest common factor of #2x^2#:

#2x^2(x+6)#

#5x+30# has the greatest common factor of #5:#

#5(x+6)#

So, we obtain

#2x^2(x+6)+5(x+6)#

Now, out of this entire expression, we can factor out #(x+6),# leaving us with

#(2x^2+5)(x+6)#