SOLUTION: factor by grouping, if possible, and check w^3 + 7w^2 + 4w + 28 Factor completely. If a polynomial is prime, state this 28a^2 - 23a - 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor by grouping, if possible, and check w^3 + 7w^2 + 4w + 28 Factor completely. If a polynomial is prime, state this 28a^2 - 23a - 2      Log On


   

Question 750580: factor by grouping, if possible, and check
w^3 + 7w^2 + 4w + 28
Factor completely. If a polynomial is prime, state this
28a^2 - 23a - 2
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w%5E3+%2B+7w%5E2+%2B+4w+%2B+28
First guess is try to do something with the factors of 7.
w%5E3%2B4w%2B7w%5E2%2B28
w%5E3%2B4w%2B7%28w%5E2%2B4%29

See some w factors in the other two terms
w%28w%5E2%2B4%29%2B7%28w%5E2%2B4%29

Notice two summed expressions each have a factor of w^2+4 distributed. We can reverse that distribution.
%28w%5E2%2B4%29%28w%2B7%29

And that is the fully factored form. highlight%28%28w%5E2%2B4%29%28w%2B7%29%29