# SOLUTION: How to find a “third” first-degree factor of x^3 + 6x^2 – 7x – 60

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 Question 264952: How to find a “third” first-degree factor of x^3 + 6x^2 – 7x – 60Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!How to find a “third” first-degree factor of ``` Since the coefficient of the highest power of x is 1, then if there ia a first degree factor, it will be of the form x ± r where r is a factor of the absolute value of the constant term, which in this case is -60. So we list the factors of |-60|, or 60. They are 1,2,3,4,5,6,10,12,15,20,30,60 try 1, using synthetic division: 1 | 1 6 -7 -60 | 1 7 0 1 7 0 -60 Nope, that leaves -60 remainder. try 2, using synthetic division: 2 | 1 6 -7 -60 | 2 16 18 1 8 9 -42 Nope, that leaves -42 remainder. try 3, using synthetic division: 3 | 1 6 -7 -60 | 3 27 60 1 9 20 0 Yep! That leaves a 0 remainder. Therefore we have factored as We got the coefficients in the second parentheses from the numbers 1 9 20 at the bottom of the synthetic division above. Now we can factor the second parentheses as And the final factored form is Edwin```