Factorization. still...

Question

Im sure im missing something. Using X as the common factor

6x³ - 2x² + ¹/_X²

My attempt:

x²(6x - 2 + ¹/_x)

But the textbook answer shows it as

x²(6x² - 2x + ¹/_X³)

Im not sure i agree, but im not 100% sure why. In my opinion if you take x² from 6x³ You should be left with 6x, not 6x². The same thought applies to the 2 and 1/x. please help

Answer 1

I agree with you on the first two terms, and neither of you on the third term. It is easier to think of if you use a negative exponent for the third term... if you factor out x² you are subtracting 2 from each exponent of x... you would have X^-2-2 = X^-4 and 1/x⁴ for the third term. The book's answer would be correct if they had simply an X, not X², as the factor.

I prefer to teach this kind of factoring by dividing each term by the desired factor, X² in this case. When you get to the fraction 1/x you have to divide by using the KeepChangeFlip model and you will get the right answer.