SOLUTION: Use long division of polynomials to divide and write the following improper rational function as a polynomial plus a rational function: a.) {{{ ( 2x^(3)-7x^(2)+7x ) / ( 2x-5 ) }

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use long division of polynomials to divide and write the following improper rational function as a polynomial plus a rational function: a.) {{{ ( 2x^(3)-7x^(2)+7x ) / ( 2x-5 ) }      Log On


   

Question 1047962: Use long division of polynomials to divide and write the following improper rational function as a polynomial plus a rational function:
a.) +%28+2x%5E%283%29-7x%5E%282%29%2B7x+%29+%2F+%28+2x-5+%29+
and
b.) +%28+4x%5E%283%29-x%5E%282%29%2B16x+%29+%2F+%28+x%5E%282%29%2B4+%29+
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
This works about the same way as regular base-ten long division. I will only do question "b". 
                 4x            -1
         _____________________________________________
         |
         |       4x^3         -x^2       +16x      +0
x^2+4    |
         |      4x^3           0x^2      16x
          -------------------------------------
                 0            -x^2       0x         0
                              -x^2      0x         -4
                            --------------------------
                                0        0         4

Main quotient is 4x-1 and remainder is 4; and since the denominator is same as the divisor, full quotient result is 4x-1%2B4%2F%28x%5E2%2B4%29.