SOLUTION: 6x^2+13x-5=

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Question 244029: 6x^2+13x-5=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor.


Looking at the expression 6x%5E2%2B13x-5, we can see that the first coefficient is 6, the second coefficient is 13, 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 13?


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)
2*(-15)
3*(-10)
5*(-6)
(-1)*(30)
(-2)*(15)
(-3)*(10)
(-5)*(6)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 13:


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 -2 and 15 add to 13 (the middle coefficient).


So the two numbers -2 and 15 both multiply to -30 and add to 13


Now replace the middle term 13x with -2x%2B15x. Remember, -2 and 15 add to 13. So this shows us that -2x%2B15x=13x.


6x%5E2%2Bhighlight%28-2x%2B15x%29-5 Replace the second term 13x with -2x%2B15x.


%286x%5E2-2x%29%2B%2815x-5%29 Group the terms into two pairs.


2x%283x-1%29%2B%2815x-5%29 Factor out the GCF 2x from the first group.


2x%283x-1%29%2B5%283x-1%29 Factor out 5 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.


%282x%2B5%29%283x-1%29 Combine like terms. Or factor out the common term 3x-1

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Answer:


So 6x%5E2%2B13x-5 factors to %282x%2B5%29%283x-1%29.


In other words, 6x%5E2%2B13x-5=%282x%2B5%29%283x-1%29


Note: you can check the answer by FOILing %282x%2B5%29%283x-1%29 to get 6x%5E2%2B13x-5 or by graphing the original expression and the answer (the two graphs should be identical).