SOLUTION: Factor: (4x^3)-(24x^2)-x+6

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Question 217217: Factor:
(4x^3)-(24x^2)-x+6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E3-24x%5E2-x%2B6 Start with the given expression


%284x%5E3-24x%5E2%29%2B%28-x%2B6%29 Group like terms


4x%5E2%28x-6%29-1%28x-6%29 Factor out the GCF 4x%5E2 out of the first group. Factor out the GCF -1 out of the second group


%284x%5E2-1%29%28x-6%29 Since we have the common term x-6, we can combine like terms


%282x%2B1%29%282x-1%29%28x-6%29 Factor 4x%5E2-1 using the difference of squares to get %282x%2B1%29%282x-1%29


So 4x%5E3-24x%5E2-x%2B6 factors to %282x%2B1%29%282x-1%29%28x-6%29


In other words, 4x%5E3-24x%5E2-x%2B6=%282x%2B1%29%2A%282x-1%29%2A%28x-6%29