Question 202586: Need help with this factoring equation:
3x^2-17xy+24y^2
My try:9x-17xy+576y ?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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Looking at  we can see that the first term is  and the last term is  where the coefficients are 3 and 24 respectively.
Now multiply the first coefficient 3 and the last coefficient 24 to get 72. Now what two numbers multiply to 72 and add to the middle coefficient -17? Let's list all of the factors of 72:
Factors of 72:
1,2,3,4,6,8,9,12,18,24,36,72
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 72
1*72
2*36
3*24
4*18
6*12
8*9
(-1)*(-72)
(-2)*(-36)
(-3)*(-24)
(-4)*(-18)
(-6)*(-12)
(-8)*(-9)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -17? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -17
| First Number | Second Number | Sum | | 1 | 72 | 1+72=73 | | 2 | 36 | 2+36=38 | | 3 | 24 | 3+24=27 | | 4 | 18 | 4+18=22 | | 6 | 12 | 6+12=18 | | 8 | 9 | 8+9=17 | | -1 | -72 | -1+(-72)=-73 | | -2 | -36 | -2+(-36)=-38 | | -3 | -24 | -3+(-24)=-27 | | -4 | -18 | -4+(-18)=-22 | | -6 | -12 | -6+(-12)=-18 | | -8 | -9 | -8+(-9)=-17 |
From this list we can see that -8 and -9 add up to -17 and multiply to 72
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
In other words, 
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Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
First thing: There is no equation here. That is because there is no equals sign anywhere to be seen. What you want to do is to factor the polynomial expression.
You have a trinomial which suggests that it is the product of two binomials. In order for the first term to be  , the first terms of the two binomials must be  and  , so start with:
(x\ \ \ ))
The next thing to notice is that the last term in your polynomial has a positive sign. That means that the two signs in the binomials must be the same sign. Since the sign on the second term in your polynomial is negative, those two signs must be negative, so now you have:
(x\ -\ \ ))
The second terms of the binomials must be of the form  and  where  . Therefore, possibilities for  and  are 1 and 24, 2 and 12, 3 and 8, and 4 and 6 and we know that 3 times one of the pair of numbers plus 1 times the other of the pair of numbers must equal 17, so:
3 times 1 = 3 plus 24 is 27, not 17
3 times 24...well never mind
3 times 2 = 6 plus 12 is 18, closer but no cigar
3 times 12...again no good
3 times 3 = 9 plus 8 is 17: Ah Ha!
So:
(x\ -\ 3y))
Check the work using FOIL:
Put 'em together:
Answer checks.
John
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