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Start with the given expression
Factor out the GCF
Sort the terms
we can see that the first term is
and the last term is
where the coefficients are 1 and 2 respectively.
Now multiply the first coefficient 1 and the last coefficient 2 to get 2. Now what two numbers multiply to 2 and add to the middle coefficient -5? Let's list all of the factors of 2:
Factors of 2:
-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 2
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5
|First Number||Second Number||Sum|
None of these pairs of factors add to -5. So the inner expression cannot be factored
So that means