SOLUTION: please help factor out.n^2-11n-80 thanks

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Question 192309: please help factor out.n^2-11n-80

thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression n%5E2-11n-80, we can see that the first coefficient is 1, the second coefficient is -11, and the last term is -80.


Now multiply the first coefficient 1 by the last term -80 to get %281%29%28-80%29=-80.


Now the question is: what two whole numbers multiply to -80 (the previous product) and add to the second coefficient -11?


To find these two numbers, we need to list all of the factors of -80 (the previous product).


Factors of -80:
1,2,4,5,8,10,16,20,40,80
-1,-2,-4,-5,-8,-10,-16,-20,-40,-80


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -80.
1*(-80)
2*(-40)
4*(-20)
5*(-16)
8*(-10)
(-1)*(80)
(-2)*(40)
(-4)*(20)
(-5)*(16)
(-8)*(10)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -11:


First NumberSecond NumberSum
1-801+(-80)=-79
2-402+(-40)=-38
4-204+(-20)=-16
5-165+(-16)=-11
8-108+(-10)=-2
-180-1+80=79
-240-2+40=38
-420-4+20=16
-516-5+16=11
-810-8+10=2



From the table, we can see that the two numbers 5 and -16 add to -11 (the middle coefficient).


So the two numbers 5 and -16 both multiply to -80 and add to -11


Now replace the middle term -11n with 5n-16n. Remember, 5 and -16 add to -11. So this shows us that 5n-16n=-11n.


n%5E2%2Bhighlight%285n-16n%29-80 Replace the second term -11n with 5n-16n.


%28n%5E2%2B5n%29%2B%28-16n-80%29 Group the terms into two pairs.


n%28n%2B5%29%2B%28-16n-80%29 Factor out the GCF n from the first group.


n%28n%2B5%29-16%28n%2B5%29 Factor out 16 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28n-16%29%28n%2B5%29 Combine like terms. Or factor out the common term n%2B5

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Answer:


So n%5E2-11n-80 factors to %28n-16%29%28n%2B5%29.


Note: you can check the answer by FOILing %28n-16%29%28n%2B5%29 to get n%5E2-11n-80 or by graphing the original expression and the answer (the two graphs should be identical).