How do you divide #(x^4+2x^3+ 5 x^2-4x-2)/(x+2) #?

1 Answer
Apr 20, 2017

#x^3+5x-14+26/(x+2)#

Explanation:

I'd like to use synthetic division for #color(red)(1)x^4+color(blue)(2)x^3+color(purple)(5)x^2+color(green)(-4)x+color(orange)(-2)#

#color(black)(-2)color(black)(|)color(red)(1)color(white)(-)color(blue)(2)color(white)(-)color(purple)(5)color(white)(.)color(green)(-4)color(white)(.)color(orange)(-2)#
#color(white)(-2)color(black)(|)color(white)(1)color(white)(.)color(black)(-2)color(white)(-)color(black)(0)color(white)(.)color(black)(-10)color(white)(.)color(black)(28)#
#color(white)(-2.)..........................................#
#color(white)(-2)color(black)(|)color(black)(1)color(white)(-)color(black)(0)color(white)(-)color(black)(5)color(white)(.)color(black)(-14)color(white)(.)color(black)(26)#

We have a remainder, but that's not a problem :)

#x^3+0x^2+5x-14+26/(x+2)#
#x^3+5x-14+26/(x+2)#