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. n%5E2-36n%2B320 This question is from textbook Intermediate Algebra

Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to factor this?



Looking at n%5E2-36n%2B320 we can see that the first term is n%5E2 and the last term is 320 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 n%5E2-36n%2B320, replace -36n with -16n%2B-20n (notice -16n%2B-20n adds up to -36n. So it is equivalent to -36n)

n%5E2%2Bhighlight%28-16n%2B-20n%29%2B320


Now let's factor n%5E2-16n-20n%2B320 by grouping:


%28n%5E2-16n%29%2B%28-20n%2B320%29 Group like terms


n%28n-16%29-20%28n-16%29 Factor out the GCF of n out of the first group. Factor out the GCF of -20 out of the second group


%28n-20%29%28n-16%29 Since we have a common term of n-16, we can combine like terms

So n%5E2-16n-20n%2B320 factors to %28n-20%29%28n-16%29


So this also means that n%5E2-36n%2B320 factors to %28n-20%29%28n-16%29 (since n%5E2-36n%2B320 is equivalent to n%5E2-16n-20n%2B320)

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Answer:

So n%5E2-36n%2B320 factors to %28n-20%29%28n-16%29