Math Worksheets

Archive for June, 2009

Question: Factor the polynomial completely?

I need some help with this question on my math worksheet. I don’t know how to do this one. Can you help me?

17. Factor the polynomial completely.
21a^2bc + 27ab + 21b^2c + 3abc

A. 3b(7a^2c + 9a + 7c + ac)
B. 3ab(7ac + 9 + 7bc + c)
C. 3b(7a^2c + 9a + 7bc + ac)
D. 3a(7abc + 9b + 7b^2c + bc)

If you answer, could you provide how you arrived at this conclusion? Thanks.

Answer: The answer is C.

Muliplying it out works as follows:

3b(7a^2c + 9a + 7bc + ac)

= [3b * 7a^2c] + [3b * 9a] + [3b * 7bc] + [3b * ac]

= [21 a^2 bc ] + [27 ab ] + [21 b^2 c] + [3abc]

= 21a^2bc + 27ab + 21b^2c + 3abc

None of the other answers multiply out to give this same answer.