SOLUTION: The problem says factor: x^2-25 x^2-7x-12 I forgot how to factor these so maybe if you just explain it briefly I might remember,thank you.

Question 90319: The problem says factor:
x^2-25
x^2-7x-12
I forgot how to factor these so maybe if you just explain it briefly I might remember,thank you.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Ah yes...factoring!!
1) Factor:
Look at each term and notice that they are both "perfect squares".

This suggests that the factors will be of the form:
which would get you when multiplied.
So, in this case, n = 5 so the factors are:

2) Factor:

The factors will have the form: where:
and

The two numbers come to mind are 3 and 4 becuase:
and

Now all you have to do is to make sure the signs of the two numbers, n and m, will give the correct signs (negative, in this case) for the sum and the product.
But, there is a problem!
To get a product of -12, the 3 and the 4 must have opposite signs, right?
But if the 3 and the 4 have opposite signs, then their sum can never be -7, can it?
So, scrap the 3 and the 4.
What other factors of 12 are there?
-1*12 or 1*-12
-2*6 or 2*-6
Looking at these factors, there's no way you are going to get a sum -7
So, you have to say that:
is prime! (Not factorable)
Now if your expression had been:
then you could factor this as:

But it isn't, so you can't!

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