Only need an answer- algebra 2

Question

4x^4+2x^3+x^2-3x+5/x-2

Answer 1

See this question  

 

https://www.wyzant.com/resources/answers/179723/only_need_a_quick_answer_to_algebra_2_question  

 

for an example of how to do polynomial long division 

Answer 2

Hi Billy,

 

One way to solve this equation would be to use long division and divide the top by x - 2. A second method would be to use synthetic division. You would turn x - 2 into an actual x value and divide the top by that x value.  

Answer 3

Billy, you really need to include parentheses to show the grouping.

The way you have this polynomial entered is way different than the

way it actually is.  This should be written as:

 

(4x⁴+2x³+x²-3x+5)/(x-2)

 

Long division with polynomials ....

 

         4x³ + 10x² + 21x + 39

        ____________________

(x-2)|  4x⁴ + 2x³ + x² - 3x + 5     Multiply x-2 by whatever makes 

        -(4x⁴ -8x³)                         x=4x⁴ ..first part of answer 4x³

         ----------------------------

                10x³ + x² - 3x + 5      Now multiply x-2 by 10x² to make

              -(10x³ -20x²)                x=10x³

             ------------------------

                       21x² - 3x + 5      Multiply by x-2 by 21x to make

                    -(21x² -42x)           x = 21x²

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

                              39x + 5       Multiply by 39 to get your x equal to 39x

                           -(39x -78)

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

                                     83       Remainder.  Since the power here is

                                                less than the power of the divisor x-2

 

Final answer:   4x³ + 10x² + 21x + 39 Remainder 83

 

Or:  4x³ + 10x² + 21x + 39 + 83/(x-2)