SOLUTION: I don't understand how to do problems that include three or four problems together such as x^3+5x^2-16x-80 can you help or explain

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I don't understand how to do problems that include three or four problems together such as x^3+5x^2-16x-80 can you help or explain       Log On


   

Question 592787: I don't understand how to do problems that include three or four problems together such as x^3+5x^2-16x-80 can you help or explain
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor.



x%5E3%2B5x%5E2-16x-80 Start with the given expression


%28x%5E3%2B5x%5E2%29%2B%28-16x-80%29 Group the terms in two pairs


x%5E2%28x%2B5%29-16%28x%2B5%29 Factor out the GCF x%5E2 out of the first group. Factor out the GCF -16 out of the second group


%28x%5E2-16%29%28x%2B5%29 Since we have the common term x%2B5, we can combine like terms


%28x-4%29%28x%2B4%29%28x%2B5%29 Now factor x%5E2-16 to get %28x-4%29%28x%2B4%29 by using the difference of squares formula.


So x%5E3%2B5x%5E2-16x-80 factors to %28x-4%29%28x%2B4%29%28x%2B5%29


In other words, x%5E3%2B5x%5E2-16x-80=%28x-4%29%28x%2B4%29%28x%2B5%29 for all values of x.


--------------------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
--------------------------------------------------------------------------------------------------------------

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I don't understand how to do problems that include three or four problems together such as x^3+5x^2-16x-80 can you help or explain.
**
Usually, but not always, problems like this with 4 terms are set up so you can factor the expression by a method called grouping:
x^3+5x^2-16x-80
Group terms to get a common factor
=x^2(x+5)-16(x+5)
factor out common term (x+5)
=(x+5)(x^2-16)
expand difference of squares
=(x+5)(x+4)(x-4)