Simple Algebra Question

1. Dec 7, 2016

krbs

Hi guys, there's a sample problem in m textbook where they simplify an expression from x3-6x2+12x-8/x2-4x+4 to (x-2)3/(x-2)2. Can you explain how they solved this? For reference, I'm learning about limits

Last edited: Dec 7, 2016
2. Dec 7, 2016

Staff: Mentor

I moved the thread to our homework section as the problem is homework-like.

I guess you mean (x3-6x2+12x-8)/(x2-4x+4). For the denominator, you should be able to find roots, once you know where the denominator gets zero you can also write it as product (here: (x-2)(x-2)). For the numerator, guess a root, then take it out as factor and compute the other factor, then do the same as for the denominator.

3. Dec 7, 2016

hilbert2

Knowledge of the fact that one root of a cubic polynomial with integer coefficients is a divisor of the constant term (here 8) will help in guessing.

4. Dec 7, 2016

krbs

Uh, yeah, I missed the big notice at the top... Had a couple glasses of wine

Ok, so I guessed root 2 (lol). Would I then just divide out factor (x-2), like polynomial long division, or is there an easier way I'm overlooking?

5. Dec 7, 2016

Staff: Mentor

Polynomial long division is the right approach - unless you directly see or guess that the numerator is (x-2)3 (possible with practice), then you can skip those steps.

6. Dec 7, 2016

krbs

Ok thank you!