SOLUTION: 2b^4+14b^3-16b-112

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Question 499737:
2b^4+14b^3-16b-112

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.




2b%5E4%2B14b%5E3-16b-112 Start with the given expression


%282b%5E4%2B14b%5E3%29%2B%28-16b-112%29 Group the terms in two pairs.


2b%5E3%28b%2B7%29-16%28b%2B7%29 Factor out the GCF 2b%5E3 out of the first group. Factor out the GCF -16 out of the second group


%282b%5E3-16%29%28b%2B7%29 Since we have the common term b%2B7, we can combine like terms


2%28b%5E3-8%29%28b%2B7%29 Factor out the GCF 2 from the first group.


2%28b-2%29%28b%5E2%2B2b%2B4%29%28b%2B7%29 Factor b%5E3-8 using the difference of cubes formula.


So 2b%5E4%2B14b%5E3-16b-112 factors to 2%28b-2%29%28b%5E2%2B2b%2B4%29%28b%2B7%29


In other words, 2b%5E4%2B14b%5E3-16b-112=2%28b-2%29%28b%5E2%2B2b%2B4%29%28b%2B7%29