How do you divide (x^4-3x^2+12)div(x+1)(x43x2+12)÷(x+1)?

2 Answers
Oct 16, 2017

Remainder: 1010

Explanation:

Using the Remainder Theorem, substitute x=-1x=1 into the equation.

f(-1)=(-1)^4-3(-1)^2+12f(1)=(1)43(1)2+12
=10=10

The remainder is 1010.

Oct 16, 2017

color(magenta)(x^3-x^2-2x+2x3x22x+2 and remainder of color(magenta)(10/(x+1)10x+1

Explanation:

color(white)(.......)color(white)(..)color(magenta)(x^3-x^2-2x+2
x+1|overline(x^4+0-3x^2+0+12)
color(white)(............)ul(x^4+x^3)
color(white)(...............)-x^3-3x^2
color(white)(................)ul(-x^3-x^2)
color(white)(.......................)-2x^2+0
color(white)(.........................)ul(-2x^2-2x)
color(white)(......................................)2x+12
color(white)(.......................................)ul(2x+2)
color(white)(..............................................)10

color(magenta)((x^4+3x^2+12) / (x+1) = x^3-x^2-2x+2 and remainder of color(magenta)(10/(x+1)