Question

Use the grouping method to factor this polynomial completely. 2x 3 + 6x 2 + 5x + 15

your answer choices are
A. (2x^2+ 5)(x + 3)
B. (2x^2+ 5)(x + 5)
C. (2x^2+ 3)(x + 5)
D. (2x^2 + 3)(x + 3)

Answer 1

A

Explanation:

Group the 4 terms into groups of 2 without changing their order. That looks like this:

`(2x^3+6x^2)+(5x+15)`

Now within each group pull out what's common:

`2x^2(x+3)+5(x+3)`

Now we have (x + 3) common between the 2 terms, so let's pull that out. With grouping, you know that it "works" if what's in the parenthesis are both exactly the same term. Ours are both (x + 3). What's "left over" are the things we originally pulled out, so group those together and you're done!

`(x+3)(2x^2+5)`