SOLUTION: factor x^2+5x-66 x2-13xy+40y^2

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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 NumberSecond NumberSum
1-661+(-66)=-65
2-332+(-33)=-31
3-223+(-22)=-19
6-116+(-11)=-5
-166-1+66=65
-233-2+33=31
-322-3+22=19
-611-6+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 NumberSecond NumberSum
1401+40=41
2202+20=22
4104+10=14
585+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)
=====================
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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