How do you find the quotient #(6t^3-9t^2+6)div(2t-3)# using long division?

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Answer 1 · 2017-05-31T15:52:39

The quotient is #=3t^2# and the remainder #=6#

We perform a long division

#color(white)(aaaa)##2t-3##color(white)(aaaa)##|##6t^3-9t^2+0t+6##color(white)(aaaa)##|##3t^2#

#color(white)(aaaaaaaaaaaaaaa)##6t^3-9t^2#

#color(white)(aaaaaaaaaaaaaaaaaa)##0-0+0t+6#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaa)##+6#

The quotient is #=3t^2# and the remainder #=6#

#(6t^3-9t^2+6)/(2t-3)=3t^2+6/(2t-3)#