State the quotient and remainder when the first polynomial is divided by the second. 3x^4-3x^3-11x^2+6x-1; x^3+x^2-2

, and . Subtracting this from the numerator leaves a remainder of

, and . Subtracting this from the previous remainder gives a new remainder of

has no factors of , so we stop here. Then

Q = 3x – 6; R = -5x² + 12x - 13

Step-by-step explanation:

One way is to use long division.

                 3x    - 6                                                

x³ + x² - 2) 3x⁴  - 3x³ - 11x² +    6x -  1

                 3x⁴ + 3x³           -    6x    

                       -  6x³ - 11x²  + 12x  -  1

                       -  6x³ - 6x²            + 12

                                 - 5x²  + 12x  - 13

Quotient = 3x – 6; Remainder = -5x²+ 12x - 13