Just a few questions I am having trouble with here before my exam:
Factorize
(1) p^6-64
(2) 25e^2-30ef-16f^2
(3) 2a^2-2b^2+5a+2am-5b-2bm
Thanks for the help.
1. .
Try the rest. For the first one I used the rational roots theorem and synthetic division to find the roots. Then used polynomial long division.
So: are canidates for possible rational roots.
2. For this one, it is just like factoring a regular quadratic equation like .
3. I am not sure that this can be factored.
We can be a bit more analytic than using the rational roots theorem. There are two ways of looking at this one:
First:
Now,
So
Thus
Second:
Now, is not particularly easy to factor, but note that:
(Just adding 0 to the expression)
<-- The difference of two squares
So again we get:
-Dan
We can try a variety of things here:
One way is:
Now complete the square on the first two terms. We have to add to each term so:
(The second factor of 2 comes from the fact that each of the first two factors is multiplied by 2. If you doubt me, expand it all out. You'll see that I'm just adding a total of 0 to the expression.)
Another way is:
<-- Again complete the square:
-Dan