SOLUTION: how do I factor -5t^2+40t-35 completely?

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Question 850615: how do I factor -5t^2+40t-35 completely?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-5t%5E2%2B40t-35

-5%28t%5E2-8t%2B7%29

-5%28t%5E2-t-7t%2B7%29 See Special Note below

-5%28%28t%5E2-t%29%2B%28-7t%2B7%29%29

-5%28t%28t-1%29%2B%28-7t%2B7%29%29

-5%28t%28t-1%29-7%28t-1%29%29

-5%28t-7%29%28t-1%29


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-5t%5E2%2B40t-35 completely factors to -5%28t-7%29%28t-1%29

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Special Note: You need to find two numbers that multiply to 7 (last term in t%5E2-8t%2B7) and that also add to -8 (middle coefficient in t%5E2-8t%2B7). These two numbers are -1 and -7. So that's why -8t breaks up into -t-7t. From there, we factor by grouping.