SOLUTION: How does one factor a polynomial where only two of items have negative exponents? 3x^-2 -7x^-1 -6 = 0 1/3x^2 - 1/7x - 6 = 0 Foil would give (1/3x - 3) (x + 2) - but how to

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: How does one factor a polynomial where only two of items have negative exponents? 3x^-2 -7x^-1 -6 = 0 1/3x^2 - 1/7x - 6 = 0 Foil would give (1/3x - 3) (x + 2) - but how to      Log On


   

Question 211128: How does one factor a polynomial where only two of items have negative exponents?
3x^-2 -7x^-1 -6 = 0
1/3x^2 - 1/7x - 6 = 0
Foil would give (1/3x - 3) (x + 2) - but how to get that - 1/7x in the middle (I can get - 7/3x)?
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
Simple, you don't factor polynomials with negative exponents. You put the negative exponents in the denominator and the get a common denominator and solve that way. You will end up having to factor but the exponents will be positive.

3x^-2 -7x^-1 -6 = 0
3%2Fx%5E2+-+7%2Fx+-+6+=+0

The common denominator on this problem is going to be x^2 so multiply the second part of the equation by x and the 6 by x^2. This will get us:

%283+-+7x+-+6x%5E2%29%2Fx%5E2+=+0

Now we multiply both sides by x^2 and that leaves us with the following polynomial:

3 - 7x - 6x^2 = 0

Now we solve this like any regular polynomial.

3 - 7x - 6x^2 = 0
6x^2 + 7x - 3 = 0
(2x+3)(3x-1) = 0
2x+3 = 0 and 3x-1 = 0
x = -3/2 and x = 1/3

I will leave the second equation for you to do but its solved in a similar manor.