SOLUTION: what is the factorization of -12x squareed+147?

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Question 178629: what is the factorization of -12x squareed+147?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-12x%5E2%2B147 Start with the given expression


-3%284x%5E2-49%29 Factor out the GCF -3


Now let's focus on the inner expression 4x%5E2-49


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4x%5E2-49 Start with the given expression.


%282x%29%5E2-49 Rewrite 4x%5E2 as %282x%29%5E2.


%282x%29%5E2-%287%29%5E2 Rewrite 49 as %287%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=2x and B=7.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%282x%29%5E2-%287%29%5E2=%282x%2B7%29%282x-7%29 Plug in A=2x and B=7.


So this shows us that 4x%5E2-49 factors to %282x%2B7%29%282x-7%29.


In other words 4x%5E2-49=%282x%2B7%29%282x-7%29.
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So -3%284x%5E2-49%29 then factors to -3%282x%2B7%29%282x-7%29


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Answer:

So -12x%5E2%2B147 completely factors to -3%282x%2B7%29%282x-7%29


In other words, -12x%5E2%2B147=-3%282x%2B7%29%282x-7%29