Question 227503: I need to factorize this match how can i do this
cd + cf
8x - 12
3x + 9
m2 - n2
t2 - 25s2
25c2 + 9d2
x2 + 3x + 2
x2 - 8x + 7
x2 - 2x - 3
3a2 + 15a + 18
A. (3a +6)(a + 3)
B. No factoriza es primo.
C. (t - 5s)(t + 5s)
D. 4(2x - 3)
E. (m + n)(m - n)
F. 3(x + 3)
G. c(d + f)
H. (x + 1)(x - 2)
I. (x + 1)(x - 3)
J. (x - 1)(x - 7)
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! You should start by FACTORING each of the items that you listed:
Take out a COMMON FACTOR of c:
cd + cf=c(d+f)
Take out a common factor of 4:
8x - 12 =4(2x-3)
Take out a common factor of 3:
3x + 9 =3(x+3)
The next two problems are the difference of two squares:
m^2 - n^2
(_____)(_____)
(m____)(m____)
(m-n)(m+n)
t^2 - 25s^2
(_____)(_____)
(t____)(t____)
{t-5s)(t+5s)
The next problem is the SUM of two squares, and this does not factor. I think you say, "Es primo!"
25c2 + 9d2
The next three are Trinomials. See my note below, and look for my explanation on "Factoring Trinomials."
x2 + 3x + 2
(_____)(_____)
(x____)(x____)
(x+2)(x+1)
x2 - 8x + 7
(_____)(_____)
(x____)(x____)
(x-7)(x-1)
x2 - 2x - 3
(_____)(_____)
(x____)(x____)
(x-3)(x+1)
In this last one, you must first take out a COMMON FACTOR:
3a2 + 15a + 18
3(a2 +5a +6)
Then factor the trinomial:
3(a+3)(a+2)
I might add that in your multiple choice answers, the answer that is given for this problem is (3a+6)(a+3), which is really NOT factored completely, and the answer that I gave you is actually BETTER than the one given to you in multiple choice format. THEIR answer is usually NOT considered correct!
Now, YOU do the matching exercise!!
You really need to see my Lessons on Factoring, especially the ones on FACTORING THE COMMON FACTOR and FACTORING TRINOMIALS. Go to my own website by doing a "Bing" or "Google" search for my last name "Rapalje". Look for and click on "Rapalje Homepage" at or near the top of the search results. Near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time." Select "Basic Algebra" and look in Chapter 2, for several sections related to "Factoring." I also have lots of problems solved in my "MATH IN LIVING COLOR" pages that correspond to these sections. One final resource that I have are FREE videos of me teaching this in my own classroom a few years ago. To see my videos, go back to my homepage, and look for "Rapalje Videos". This is all free.
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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