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

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

How do you use the grouping method to factor 2x^3 + 12 x^2 + 5x + 302x^3 + 12 x^2 + 5x + 30 completely?