SOLUTION: factor 12s2+11s-5

Question 402893: factor 12s2+11s-5
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 12 and -5 respectively.

Now multiply the first coefficient 12 and the last coefficient -5 to get -60. Now what two numbers multiply to -60 and add to the middle coefficient 11? Let's list all of the factors of -60:

Factors of -60:
1,2,3,4,5,6,10,12,15,20,30,60

-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -60
(1)*(-60)
(2)*(-30)
(3)*(-20)
(4)*(-15)
(5)*(-12)
(6)*(-10)
(-1)*(60)
(-2)*(30)
(-3)*(20)
(-4)*(15)
(-5)*(12)
(-6)*(10)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11

First Number	Second Number	Sum
1	-60	1+(-60)=-59
2	-30	2+(-30)=-28
3	-20	3+(-20)=-17
4	-15	4+(-15)=-11
5	-12	5+(-12)=-7
6	-10	6+(-10)=-4
-1	60	-1+60=59
-2	30	-2+30=28
-3	20	-3+20=17
-4	15	-4+15=11
-5	12	-5+12=7
-6	10	-6+10=4

From this list we can see that -4 and 15 add up to 11 and multiply to -60

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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