Question 407530: x^2-12x+20
It's asking me to factor this
and that is x squared minus 12x plus 20
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 20 respectively.
Now multiply the first coefficient 1 and the last coefficient 20 to get 20. Now what two numbers multiply to 20 and add to the middle coefficient -12? Let's list all of the factors of 20:
Factors of 20:
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 20
1*20
2*10
4*5
(-1)*(-20)
(-2)*(-10)
(-4)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12
| First Number | Second Number | Sum | | 1 | 20 | 1+20=21 | | 2 | 10 | 2+10=12 | | 4 | 5 | 4+5=9 | | -1 | -20 | -1+(-20)=-21 | | -2 | -10 | -2+(-10)=-12 | | -4 | -5 | -4+(-5)=-9 |
From this list we can see that -2 and -10 add up to -12 and multiply to 20
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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Answer:
So  factors to
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Jim
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