g(x)=2x^6+3x^4-x^2+3
g(2) =>x=2
factor will be (x-2)
........(2x^5+4x^4+11x^3+22x^2+43x +86
(x-2)|2x^6+0*x^5+3x^4+0*x^3-x^2+0*x+3
........2x^6-4x^5
.................4x^5+3x^4
.................4x^5-8x^4
..........................11x^4+0*x^3
..........................11x^4-22x^3
.....................................22x^3-x^2
.....................................22x^3-44x^2
.................................................43x^2+0*x
.................................................43x^2-86x
.............................................................86x+3
.............................................................86x-172
....................................................................172->reminder
which proves that g(2) =172