Wow! I'm almost ready to take the Algebra placement test. It took me literally a 2 weeks to learn how to factor Polynomials. I was up until 1:00 AM solving this monster. I found that documenting each problem has been key to my learning. Anyways here it is.
12x^2 + 12x + 3
a. What 2 numbers added together equal the middle term 12?
(6)+(6) =12
b. When the 1st and the 3rd terms are multiplied together, does this equal the
product of (12)(3) which is 36?
(6)(6) = 36
12x^2 + (6 + 6)x + 3
12x^2 + 6x + 6x + 3
c. Now factor by grouping
12x^2 + 6x + 6x + 3
----- ---- --- --
6x 6x 3 3
6x(2x^2 + 1) 3(2x + 1)
-------------- + ------------
(2x^2 + 1) (2x + 1)
(6x + 3)(2x + 1) The 6 and 3 still have common factors so
--- -- break it down even further
3 3
----------
3(2x + 1)
ANSWER: 3(2x +1)^2
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