SOLUTION: Hello. Can you please help me? It's greatly appreciated. solve equation by factoring: 3x^2 - 13x -10 thank you!

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Question 368621: Hello. Can you please help me? It's greatly appreciated.
solve equation by factoring:
3x^2 - 13x -10 thank you!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll show you how to factor it.



Looking at we can see that the first term is and the last term is where the coefficients are 3 and -10 respectively.

Now multiply the first coefficient 3 and the last coefficient -10 to get -30. Now what two numbers multiply to -30 and add to the middle coefficient -13? Let's list all of the factors of -30:



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

-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. 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)

note: remember, the product of a negative and a positive number is a negative 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
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 this list we can see that 2 and -15 add up to -13 and multiply to -30


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!
solve equation by factoring:
3x^2 - 13x -10
====
You cannot "solve" the expression unless it is an equation.
-------------
Assume 3x^2 - 13x - 10 = 0
----
3x^2 -15x+2x -10 = 0
---
3x(x-5)+2(x-5) = 0
---
(x-5)(3x+2) = 0
x = 5 or x = -3/2
===========================
Cheers,
Stan H.
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