How do you divide #(5x^3 – 6 – 5x) ÷ (10 + 5x)#?

Question

1366 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-04T16:54:06

The remainder is #=-36# and the quotient is #=x^2-2x+3#

We perform a long division

#color(white)(aaaa)##5x+10##color(white)(aaaa)##|##5x^3+0x^2-5x-6##color(white)(aaaa)##|##x^2-2x+3#

#color(white)(aaaaaaaaaaaaaaaa)##5x^3+10x^2#

#color(white)(aaaaaaaaaaaaaaaaaa)##0-10x^2-5x#

#color(white)(aaaaaaaaaaaaaaaaaaaa)##-10x^2-20x#

#color(white)(aaaaaaaaaaaaaaaaaaaaaa)##-0+15x-6#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaa)##+15x+30#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaa)##+0-36#

The remainder is #=-36# and the quotient is #=x^2-2x+3#

#(5x^3-5x-6)/(5x+10)=x^2-2x+3-36/(5x+10)#