How do you divide #(3x^4+9x^3-2x^2+2x-7)/(x-2) #?

1 Answer
Jun 28, 2017

The remainder is #=109# and the quotient is #=3x^3+15x^2+28x+58#

Explanation:

Let's perform the synthetic division

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#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaa)##6##color(white)(aaaaaa)##30##color(white)(aaa)##56##color(white)(aaaaa)##116#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##3##color(white)(aaa)##15##color(white)(aaaaa)##28##color(white)(aaa)##58##color(white)(aaaaa)##color(red)(109)#

The remainder is #=109# and the quotient is #=3x^3+15x^2+28x+58#

Therefore,

#(3x^4+9x^3-2x^2+2x-7)/(x-2)=3x^3+15x^2+28x+58+(109)/(x-2)#