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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

Question 281596: Factor as completely as possible.
a) x%5E3-4x
b) xy-x%2B8y-8
c) x%5E3%2Bx%5E2-90x
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) About Me  (Show Source):
You can put this solution on YOUR website!
I'll knock myself out ;)
a) x%5E3-4x
b) xy-x%2B8y-8
c) x%5E3%2Bx%5E2-90x
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!
x%5E3+-+4x+=+x%28x%5E2+-+4%29 Notice how an x comes out of both terms
x%28x%5E2+-+4%29+=+x%28x%2B2%29%28x-2%29 this is binomial factoring, we can do this because there is a minus sign in between x%5E2 and 4. also, both 4 and x%5E2 can be square rooted perfectly.
So the final answer is:
highlight%28x%28x%2B2%29%28x-2%29%29
b) This example is a super use of greatest common factoring, sometimes noted as gcd:
xy-x%2B8y-8 group the first two together and the last two:
%28xy+-+x%29+%2B+%288y+-+8%29 then factor by greatest common factoring:
x%28y-1%29+%2B+8%28y+-+1%29 we can see that there are two y-1, we can factor that out too:
%28y-1%29+%28x+%2B+8%29 the easiest way to see this step is to take out the y-1 and whatever is left over is your second term.
highlight%28%28y-1%29+%28x+%2B+8%29%29 is your final answer
c) x%5E3%2Bx%5E2-90x
Once again start off with greatest common factoring, there is an x is each of those:
x%28x%5E2+%2B+x+-+90%29
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:
highlight%28x+%28x+%2B+10%29+%28x+-+9%29%29 final answer

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3-4x
for this one when u look at it theres a x in both variables so the gcf is x
x%28x%5E2-4%29 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: x%5E2-366's,x%5E2-497's,x%5E2-14412's)
highlight%28x%28x-2%29%28x%2B2%29%29 this would be completly factored


%28xy-x%29%2B%288y-8%29use group factoring
x%28y-1%29%2B8%28y-1%29factor x and 8 out
highlight%28%28x%2B8%29%28y-1%29%29add them together, completely factored


x%5E3%2Bx%5E2-90x same as first one GCF=x
x%28x%5E2%2Bx-90%29 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.
highlight%28x%28x%2B10%29%28x-9%29%29this is completely factored