SOLUTION: 6s squared- s-5 factor the trinomial

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Question 576488: 6s squared- s-5 factor the trinomial
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 6s%5E2-s-5, we can see that the first coefficient is 6, the second coefficient is -1, and the last term is -5.


Now multiply the first coefficient 6 by the last term -5 to get %286%29%28-5%29=-30.


Now the question is: what two whole numbers multiply to -30 (the previous product) and add to the second coefficient -1?


To find these two numbers, we need to list all of the factors of -30 (the previous product).


Factors of -30:
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -30.
1*(-30) = -30
2*(-15) = -30
3*(-10) = -30
5*(-6) = -30
(-1)*(30) = -30
(-2)*(15) = -30
(-3)*(10) = -30
(-5)*(6) = -30

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -1:


First NumberSecond NumberSum
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=1



From the table, we can see that the two numbers 5 and -6 add to -1 (the middle coefficient).


So the two numbers 5 and -6 both multiply to -30 and add to -1


Now replace the middle term -1s with 5s-6s. Remember, 5 and -6 add to -1. So this shows us that 5s-6s=-1s.


6s%5E2%2Bhighlight%285s-6s%29-5 Replace the second term -1s with 5s-6s.


%286s%5E2%2B5s%29%2B%28-6s-5%29 Group the terms into two pairs.


s%286s%2B5%29%2B%28-6s-5%29 Factor out the GCF s from the first group.


s%286s%2B5%29-1%286s%2B5%29 Factor out 1 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28s-1%29%286s%2B5%29 Combine like terms. Or factor out the common term 6s%2B5


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Answer:


So 6s%5E2-s-5 factors to %28s-1%29%286s%2B5%29.


In other words, 6s%5E2-s-5=%28s-1%29%286s%2B5%29.


Note: you can check the answer by expanding %28s-1%29%286s%2B5%29 to get 6s%5E2-s-5 or by graphing the original expression and the answer (the two graphs should be identical).