SOLUTION: please help me solve this equation. {{{n^2-36n+320}}}

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Question 116761This question is from textbook Intermediate Algebra
: please help me solve this equation. This question is from textbook Intermediate Algebra

Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
It is not an equation. The is no equal sign with something on the other side of it.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Do you want to factor this?



Looking at we can see that the first term is and the last term is where the coefficients are 1 and 320 respectively.

Now multiply the first coefficient 1 and the last coefficient 320 to get 320. Now what two numbers multiply to 320 and add to the middle coefficient -36? Let's list all of the factors of 320:



Factors of 320:
1,2,4,5,8,10,16,20,32,40,64,80,160,320

-1,-2,-4,-5,-8,-10,-16,-20,-32,-40,-64,-80,-160,-320 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 320
1*320
2*160
4*80
5*64
8*40
10*32
16*20
(-1)*(-320)
(-2)*(-160)
(-4)*(-80)
(-5)*(-64)
(-8)*(-40)
(-10)*(-32)
(-16)*(-20)

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


Now which of these pairs add to -36? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -36

First NumberSecond NumberSum
13201+320=321
21602+160=162
4804+80=84
5645+64=69
8408+40=48
103210+32=42
162016+20=36
-1-320-1+(-320)=-321
-2-160-2+(-160)=-162
-4-80-4+(-80)=-84
-5-64-5+(-64)=-69
-8-40-8+(-40)=-48
-10-32-10+(-32)=-42
-16-20-16+(-20)=-36



From this list we can see that -16 and -20 add up to -36 and multiply to 320


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 )

-------------------------------
Answer:

So factors to
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