how do you find the quotient and remainder if f(x) is divided by p(x)? f(x)=x²-3, f(x)=2x^4-x³-3x²+6x-8

Question

May you help be step by step?

Answer 1

the easiest way to find rimainder;

Let me assume that x²=3,

we may write

18 for 2x⁴

-3x for -x³ 

-9 for -3x² 

then your polinomial turns into 18-3x-9+6x-8=3x+1

 

what a surprise, it is our remainder. This process always works because of definition of polinomial division. Just try to equalize your divider to 0, take xs aside, and then replace it into divident. Do-it-yourself :)

Answer 2

                 2x² - x  + 3  (quotient)
             |———————————— 
    x² - 3 |  2x⁴ - x³ - 3x² + 6x - 8
             –
                (2x⁴       - 6x²)  
                      - x³ + 3x² + 6x           
                   –    
                      - x³          + 3x  
                               3x² + 3x - 8     
                            – 
                               3x²        - 9    
                                      3x + 1 (remainder)