SOLUTION: I did group terms and factor each group, now stuck on Distributive property for x^3+4x^2+x+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I did group terms and factor each group, now stuck on Distributive property for x^3+4x^2+x+4      Log On


   

Question 709784: I did group terms and factor each group, now stuck on Distributive property
for x^3+4x^2+x+4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3%2B4x%5E2%2Bx%2B4
Grouping:
%28x%5E3%2B4x%5E2%29%2B%28x%2B4%29
Factoring out the GCF. (Note: This point in factoring by grouping is one of the few times you actually factor out a GCF of 1!)
x%5E2%28x%2B4%29%2B1%28x%2B4%29
Now we look to see if the two groups have a common factor. (If not, then we need to try something else (factoring out the negative of the GCF from each group and/or changing the groups). But we are fortunate. The two groups do have a common factor of (x+4). Factoring out the (x+4) from the two groups:
%28x%2B4%29%28x%5E2%2B1%29

Neither factor will factor further so are finished factoring.

If you want to check, use FOIL to multiply out the answer. You should end up with x%5E3%2B4x%5E2%2Bx%2B4.