SOLUTION: Find the remainder when {{{ 3x^4+2x^3-x^2/3-x/9+2/27 }}} divided by {{{ x+2/3 }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the remainder when {{{ 3x^4+2x^3-x^2/3-x/9+2/27 }}} divided by {{{ x+2/3 }}}       Log On


   

Question 983557: Find the remainder when
+3x%5E4%2B2x%5E3-x%5E2%2F3-x%2F9%2B2%2F27+ divided by +x%2B2%2F3+
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the dividend and the divisor by 27, simplify, and then use polynomial division.

81x%5E4%2B54x%5E3-9x%5E2-3x%2B2 divided by 27x%2B18;
All whole number coefficients, much easier to handle this way.

--- 

                  3x^3       0     -(1/3)x
             |_______________________________________
             |
27x-18    |    81x^4     54x^3    -9x^2     2
               81x^4     54x^3
                _______________
               0          0        -9x^2
                          0          0
                          _____________
                                    -9x^2     2
                                    -9x^2     6
                                    __________
                                      0      -4


Quotient is highlight%283x%5E3-%281%2F3%29x-4%2F%2827x-18%29%29.