SOLUTION: The expression X^3-2x^2+3x-6 over x-2 simplified is I don't understand how to do this please help

Algebra ->  Systems-of-equations -> SOLUTION: The expression X^3-2x^2+3x-6 over x-2 simplified is I don't understand how to do this please help      Log On


   

Question 941510: The expression X^3-2x^2+3x-6 over x-2 simplified is
I don't understand how to do this please help
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First we factor x%5E3-2x%5E2%2B3x-6 by grouping


x%5E3-2x%5E2%2B3x-6


%28x%5E3-2x%5E2%29%2B%283x-6%29


x%5E2%28x-2%29%2B%283x-6%29


x%5E2%28x-2%29%2B3%28x-2%29


%28x%5E2%2B3%29%28x-2%29


-------------------------------------------------------


So x%5E3-2x%5E2%2B3x-6 factors to %28x%5E2%2B3%29%28x-2%29


-------------------------------------------------------


We then use this factorization to help simplify


%28x%5E3-2x%5E2%2B3x-6%29%2F%28x-2%29


%28%28x%5E2%2B3%29%28x-2%29%29%2F%28x-2%29


%28%28x%5E2%2B3%29highlight%28%28x-2%29%29%29%2F%28highlight%28%28x-2%29%29%29


%28%28x%5E2%2B3%29cross%28%28x-2%29%29%29%2F%28cross%28%28x-2%29%29%29


x%5E2%2B3


-------------------------------------------------------


Therefore, %28x%5E3-2x%5E2%2B3x-6%29%2F%28x-2%29 simplifies to x%5E2%2B3

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
The expression X^3-2x^2+3x-6 over x-2 simplified is
I don't understand how to do this please help


%28x%5E3+-+2x%5E2+%2B+3x+-+6%29%2F%28x+-+2%29 

%28x%5E2%28x+-+2%29+%2B+3%28x+-+2%29%29%2F%28x+-+2%29 ---- Factoring numerator

%28%28x%5E2+%2B+3%29%28x+-+2%29%29%2F%28x+-+2%29 -------- Factors of numerator are determined

%28%28x%5E2+%2B+3%29cross%28%28x+-+2%29%29%29%2Fcross%28%28x+-+2%29%29_______highlight_green%28x%5E2+%2B+3%29