How do you divide #(4x^3 + 2x -15) / (2 x^2-1 ) # using polynomial long division?

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Answer 1 · 2017-11-21T13:00:01

The quotient is #2x# and the remainder is #=4x-15#

Perform the long division

#color(white)(aaaa)##4x^3+0x^2+2x-15##color(white)(aaaa)##|##2x^2-1#

#color(white)(aaaa)##4x^3+0x^2-2x##color(white)(aaaaaaaaa)##|##2x#

#color(white)(aaaa)##0x^3+0x^2+4x-15#

The quotient is #2x# and the remainder is #=4x-15#

So,

#(4x^3+0x^2+2x-15)/(2x^2-1)=2x+(4x-15)/(2x^2-1)#