How do you factor x⁻¹-3x⁻²+2x⁻³?
I've been working on this problem for the past 30 minutes and I just can't factor it! So far, I've turned the negative exponents into fractions so that it reads like:
(1/x)-(3/x²)+(2/x³)=(1/x)[1-(3/x)+(2/x²)]
gahhh so confusing! 10 points for some help...
Update:omg thank you so much Brian. I was SOOO CLOSE! the first time I did the exact same thing you did, except I didn't realize you could factor out 1/x^3...but wow it makes perfect sense now. duhh! THANK YOU SO MUCH. =)
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Instead of factoring out 1/x, factor out 1/x^3 to give:
x^(-1) - 3x^(-2) + 2x^(-3)
= 1/x - 3/x^2 + 2/x^3
= 1/x^3 * (x^2 - 3x + 2)
= (x - 2)(x - 1)/x^3.
I hope this helps!