SOLUTION: divide the polynomials using long divisin. What is Q(x) and r(x)? (11x+20x2+12x3+2) by (3x+2) (elevenx+twentyx to the second power+ twelvex to the third power + two) divided

First write the polynomial in descending order of powers of x

12x³ + 20x² + 11x + 2

Then write

      _______________________ 
3x + 2) 12x³ + 20x² + 11x + 2

Divide the first term 12x³ by 3x: 
and write 4x² above the 20x²:

                4x²__________  
3x + 2) 12x³ + 20x² + 11x + 2

Multiply the 4x² by the (3x + 2) getting  and
write it under the first two terms and draw a line underneath:

                4x²__________  
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²  

Subtract ,
and write 12x² under the line under 8x², like this:

                4x²__________  
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x²

Now bring down the next term + llx and write in next to the 12x²

                4x²__________  
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x

Divide the first term on the bottom 12x² by 3x: 
and write + 4x above the 11x at the top, like this:

                4x² +  4x____ 
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x

Multiply the 4x by the (3x + 2) getting  and
write it under the first two terms and draw a line underneath:

                4x² +  4x____ 
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x
               12x² +  8x


Subtract ,
and write 3x under the line under 8x, like this:

                4x² +  4x____ 
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x
               12x² +  8x
                       3x

Now bring down the last term + 2 and write in next to the 3x

                4x² +  4x____ 
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x
               12x² +  8x
                       3x + 2

Divide the first term on the bottom 3x by the 3x at the left:
 and write + 1 above the + 2 at the top, 
like this:

                4x² +  4x + 1
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x
               12x² +  8x
                       3x + 2

Multiply the + 1 by the (3x + 2) getting  and
write it under the two terms at the bottom and draw a line 
underneath:

                4x² +  4x + 1
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x
               12x² +  8x
                       3x + 2
                       3x + 2

Subtract ,
and write 0 under the line under 2, like this:

                4x² +  4x + 1
3x + 2) 12x³ + 20x² + 11x + 2
        12x³ +  8x²
               12x² + 11x
               12x² +  8x
                       3x + 2
                       3x + 2
                            0

Now you are done and the answer is  and
since the remainder is 0 you do not have to put it over
the divisor  and add it on like you do when
the remainder is not 0.

Edwin