SOLUTION: factor 12s2+11s-5

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Question 402893: factor 12s2+11s-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at 12s%5E2%2B11s-5 we can see that the first term is 12s%5E2 and the last term is -5 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 NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+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 12s%5E2%2B11s-5, replace 11s with -4s%2B15s (notice -4s%2B15s adds up to 11s. So it is equivalent to 11s)

12s%5E2%2Bhighlight%28-4s%2B15s%29%2B-5


Now let's factor 12s%5E2-4s%2B15s-5 by grouping:


%2812s%5E2-4s%29%2B%2815s-5%29 Group like terms


4s%283s-1%29%2B5%283s-1%29 Factor out the GCF of 4s out of the first group. Factor out the GCF of 5 out of the second group


%284s%2B5%29%283s-1%29 Since we have a common term of 3s-1, we can combine like terms

So 12s%5E2-4s%2B15s-5 factors to %284s%2B5%29%283s-1%29


So this also means that 12s%5E2%2B11s-5 factors to %284s%2B5%29%283s-1%29 (since 12s%5E2%2B11s-5 is equivalent to 12s%5E2-4s%2B15s-5)



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Answer:
So 12s%5E2%2B11s-5 factors to %284s%2B5%29%283s-1%29