Hi, Im having difficulty factoring completely. Ive been running into this problem over again.
heres an example:
5y4 + 10y2 + 5
I ended up with:
5y(y3 + 1) 5(Y + 1)
the correct answer is:
5(y2 + 1)2
how do I know what Im supposed to completely factor? is there a rule Im fogetting? initially, I thought I was suppose to factor out all exponents but I found that not to be true.
heres another:
12p3 + 31p2 + 20p
Basically you have to play around with the factors of 12 and 20.
For 12, you could have 12&1 ; 6&2 ; 3&4
For 20, you could have 20&1 ; 10&2 ; 4&5
Then you have to see which of those coefficients are capable of making 31 for the middle term.
So write:
(We know both have to be + since the middle and last terms are positive.)
Now take those possible co-efficients, plug them in, and multiply out. If one set doesnt work, try the next.
Note that you can also swap the co-efficients around.
Instead of pairs 3&4 and 4&5 ; you could have 4&3 and 4&5.
Later on you will have the knack of instinctively knowing which it would probably be.
I can give you a hint, which is: The co-efficients will often be those close to each other. If we go back to the example of 12, it will most likely be 3&4 (or 4&3) that will work. But this is not always true.