How do you divide #(2r^3+5r^2-2r-15) div(2r-3)#?

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Answer 1 · 2017-02-15T12:28:04

The quotient is #=r^2+4r+5#

Let's do a long division

#color(white)(aaaa)##2r^3+5r^2-2r-15##color(white)(aaaa)##|##2r-3#

#color(white)(aaaa)##2r^3-3r^2##color(white)(aaaaaaaaaaaaa)##|##r^2+4r+5#

#color(white)(aaaaaa)##0+8r^2-2r#

#color(white)(aaaaaaaa)##+8r^2-12r#

#color(white)(aaaaaaaaaa)##+0+10r-15#

#color(white)(aaaaaaaaaaaaaa)##+10r-15#

#color(white)(aaaaaaaaaaaaaaaa)##+0-0#

The quotient is #=r^2+4r+5#

The remainder is #=0#