SOLUTION: x^2-12x+20 It's asking me to factor this and that is x squared minus 12x plus 20

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

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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