Question 366639: I'm having some trouble with factoring Polynomials with a coefficient in front of the squared variable. 10r2-25r-6. I've tried (2r+2)(5r-3).
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 10 and -6 respectively.
Now multiply the first coefficient 10 and the last coefficient -6 to get -60. Now what two numbers multiply to -60 and add to the middle coefficient -25? 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 -25? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -25
| 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 |
None of these pairs of factors add to -25. So the expression cannot be factored
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