SOLUTION: Factor by grouping, if possible, and show me how to check... much appreciated 8a^3 - 2a^2 + 12a – 3

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Question 621901: Factor by grouping, if possible, and show me how to check... much appreciated
8a^3 - 2a^2 + 12a – 3
Found 2 solutions by jim_thompson5910, lenny460:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8a%5E3-2a%5E2%2B12a-3 Start with the given expression


%288a%5E3-2a%5E2%29%2B%2812a-3%29 Group the terms in two pairs


2a%5E2%284a-1%29%2B3%284a-1%29 Factor out the GCF 2a%5E2 out of the first group. Factor out the GCF 3 out of the second group


%282a%5E2%2B3%29%284a-1%29 Since we have the common term 4a-1, we can combine like terms


So 8a%5E3-2a%5E2%2B12a-3 factors to %282a%5E2%2B3%29%284a-1%29


In other words, 8a%5E3-2a%5E2%2B12a-3=%282a%5E2%2B3%29%284a-1%29

Answer by lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Factor by Grouping:
8a^3 - 2a^2 + 12a - 3
(8a^3 - 2a^2) + (12a - 3)
Factor:
8a^3 - 2a^2 = 2a^2(4a - 1)
Factor:
12a - 3 = 3(4a - 1)
The Answer:
(2a^2 + 3)(4a - 1)