how do i solve this using synthetic division (2x^4+3x^3-x-6)/(x+2)

Question

how do i solve this using synthetic division (2x^4+3x^3-x-6)/(x+2)

Answer 1

Let......

f(x)=2x⁴+3x³-x-6

g(x)=x+2=(x-k).......where k=-2

 

Using synthetic division, we can write....

 

-2    2    3    0   -1   -6   .......and divide "k" into 

==================      the coefficients of f(x)

       ↓  -4    2   -4  10

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

       (2   -1    2  -5)   4

                                ↑

                         (remainder), so (-2) is "not a zero."

 

The values in the brackets are coefficients for a 

function q(x)=2x³-x²+2x-5...

 

 f(x)         (2x⁴+3x³-x-6)                                   4

-----  =    -------------------  =  (2x³-x²+2x-5) + -----

 g(x)              (x+2)                                          x+2

 

  ...and multiplying both sides by "x+2" we get...

 

f(x)   =    (2x⁴+3x³-x-6)   =  (x+2)(2x³-x²+2x-5) + 4

 

This is an illustration of the Special Case for the Division

Algorithm "f(x) = (x-k)•q(x) + r" as it includes a remainder.