SOLUTION: Factor completely. n squared - 11n + 10

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Question 114999: Factor completely.
n squared - 11n + 10
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 10 respectively.

Now multiply the first coefficient 1 and the last coefficient 10 to get 10. Now what two numbers multiply to 10 and add to the middle coefficient -11? Let's list all of the factors of 10:



Factors of 10:
1,2,5,10

-1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 10
1*10
2*5
(-1)*(-10)
(-2)*(-5)

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to -11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -11

First NumberSecond NumberSum
1101+10=11
252+5=7
-1-10-1+(-10)=-11
-2-5-2+(-5)=-7



From this list we can see that -1 and -10 add up to -11 and multiply to 10


Now looking at the expression , replace with (notice adds up to . So it is equivalent to )




Now let's factor by grouping:


Group like terms


Factor out the GCF of out of the first group. Factor out the GCF of out of the second group


Since we have a common term of , we can combine like terms

So factors to


So this also means that factors to (since is equivalent to )
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