Question 117687: factor
x^2+5x-66
x2-13xy+40y^2
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! #1
Looking at  we can see that the first term is  and the last term is  where the coefficients are 1 and -66 respectively.
Now multiply the first coefficient 1 and the last coefficient -66 to get -66. Now what two numbers multiply to -66 and add to the middle coefficient 5? Let's list all of the factors of -66:
Factors of -66:
1,2,3,6,11,22,33,66
-1,-2,-3,-6,-11,-22,-33,-66 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -66
(1)*(-66)
(2)*(-33)
(3)*(-22)
(6)*(-11)
(-1)*(66)
(-2)*(33)
(-3)*(22)
(-6)*(11)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5
| First Number | Second Number | Sum | | 1 | -66 | 1+(-66)=-65 | | 2 | -33 | 2+(-33)=-31 | | 3 | -22 | 3+(-22)=-19 | | 6 | -11 | 6+(-11)=-5 | | -1 | 66 | -1+66=65 | | -2 | 33 | -2+33=31 | | -3 | 22 | -3+22=19 | | -6 | 11 | -6+11=5 |
From this list we can see that -6 and 11 add up to 5 and multiply to -66
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
#2
Looking at  we can see that the first term is and the last term is  where the coefficients are 1 and 40 respectively.
Now multiply the first coefficient 1 and the last coefficient 40 to get 40. Now what two numbers multiply to 40 and add to the middle coefficient -13? Let's list all of the factors of 40:
Factors of 40:
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 40
1*40
2*20
4*10
5*8
(-1)*(-40)
(-2)*(-20)
(-4)*(-10)
(-5)*(-8)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -13
| First Number | Second Number | Sum | | 1 | 40 | 1+40=41 | | 2 | 20 | 2+20=22 | | 4 | 10 | 4+10=14 | | 5 | 8 | 5+8=13 | | -1 | -40 | -1+(-40)=-41 | | -2 | -20 | -2+(-20)=-22 | | -4 | -10 | -4+(-10)=-14 | | -5 | -8 | -5+(-8)=-13 |
From this list we can see that -5 and -8 add up to -13 and multiply to 40
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
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! factor
x^2+5x-66
= x^2+11x-6x-66
= x(x+11)-6(x+11)
= (x+11)(x-6)
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x2-13xy+40y^2
= x^2-5xy-8xy+40y^2
= x(x-5y)-8y(x-5y)
= (x-5y)(x-8y)
=======================
Cheers,
Stan H.
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