SOLUTION: Factor as completely as possible. a) {{{x^3-4x}}} b) {{{xy-x+8y-8}}} c) {{{x^3+x^2-90x}}} Hello! You dont have to do all three of these (unless you want too; go ahead and kno

Question 281596: Factor as completely as possible.
a)
b)
c)
Hello! You dont have to do all three of these (unless you want too; go ahead and knock yourself out ;) ) What I wanted to know was if someone could please explain to me how I would factor these as completely as possible?
Thank you
Found 2 solutions by Mathematicians, JBarnum:
Answer by Mathematicians(84) (Show Source): You can put this solution on YOUR website!
I'll knock myself out ;)
a)
b)
c)
a) We first want to look for any greatest common factors, notice there is an x in each term which is our greatest common factor!
Notice how an x comes out of both terms
this is binomial factoring, we can do this because there is a minus sign in between and . also, both and can be square rooted perfectly.
So the final answer is:

b) This example is a super use of greatest common factoring, sometimes noted as gcd:
group the first two together and the last two:
then factor by greatest common factoring:
we can see that there are two y-1, we can factor that out too:
the easiest way to see this step is to take out the y-1 and whatever is left over is your second term.
is your final answer
c)
Once again start off with greatest common factoring, there is an x is each of those:

Now we want to find two things that multiply to be negative 90 and add up to be positive 1. One number is going to have to be a negative because that is the only way to multiply two numbers to get -90. The answer for this one is -9 and +10 which reduces to our final factoring:
final answer

Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!

for this one when u look at it theres a x in both variables so the gcf is x
whats left is a perfect square inside the brackets so you can factor further, i sugest getting familiar with what squars look like to make it easier for u to factor, otherwise u will need to use the quadratic formula.(Ex: 6's,7's,12's)
this would be completly factored

use group factoring
factor x and 8 out
add them together, completely factored

same as first one GCF=x
find 2 numbers multiply to get -90 and add to get 1. -9 and +10. if u cant figure how to do this then use quadratic formula.
this is completely factored
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