How do you divide #(4x^4 -12 x^2-x-20)/((x^2 + 4) )#?

Question

1460 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-03T05:39:49

The quotient is #(4x^2-28)# and the remainder is #(-x+92)#

Perform a long division.

#color(white)(aaaa)##4x^4-12x^2-x-20##color(white)(aaaa)##|##x^2+4#

#color(white)(aaaa)##4x^4+16x^2##color(white)(aaaaaaaaaaaa)##|##4x^2-28#

#color(white)(aaaaaa)##0-28x^2-x-20#

#color(white)(aaaaaaaa)##-28x^2-0x-112#

#color(white)(aaaaaaaaaa)##+0-x+92#

The quotient is #(4x^2-28)# and the remainder is #(-x+92)#

#(4x^4-12x^2-x-20)/(x^2+4)=4x^2-28+(-x+92)/(x^2+4)#