Division of Polynomials

Question

x³-3x²+x-2√10x⁴-14x³-10x²+6x-10

 

The quotient is _______x+_______

 

The remainder is _______x²+_______x+_______

Answer 1

The problem is not stated correctly.

The polynomial on the top is degree 3 while

the bottom polynomial is degree 4. They

will not divide. Finally the square root sign is used instead of

the division symbol.

 

Perhaps what you mean is:

  10^4 - 14x^3 - 10x^2 + 6x + 10 

      divided by

 x^3 - 3x^2 + x - 2

 

At the very least, it will serve as a simple example.

                       

                              10x     + 16

                             _______________________________

x^3 - 3x^2 + x - 2 | 10x^4 - 14x^3 - 10x^2 + 6x + 10

                               10x^4 - 30x^3+ 10x^2 - 20x

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

                                           16x^3 - 20x^2 + 26x +10

                                           16x^3 - 48x^2 +16x - 32

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

                                                         28x^2 + 10x + 42

 

Now to check, we multiply the answer times the polynomial

divided by, then add the remainder:

 

  (10x+16)(x^3-3x^2+x-2) + 28x^2 + 10x + 42

 

  10x^4 - 30x^3 + 10x^2 - 20x

               16x^3 - 48x^2 + 16x - 32

                           28x^2 + 10x + 42

 

10x^4 - 14x^3 -10x^2 + 6x + 10

 

which is the original polynomial we started with.

 

Go to youtube and watch videos on how to 

DIVIDE polynomials