How do you evaluate #\frac{4x^{4}-5x^{2}+2x-10}{2x-3}#?

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Answer 1 · 2018-08-11T07:32:18

The remainder is #=2# and the quotient is #=2x^3+3x^2+2x+4#

Perform a long division

#color(white)(aaaa)##4x^4+0x^3-5x^2+2x-10##color(white)(aaaa)##|##2x-3#

#color(white)(aaaa)##4x^4-6x^3##color(white)(aaaaaaaaaaaaaaaaaa)##|##2x^3+3x^2+2x+4#

#color(white)(aaaa)##0x^4+6x^3-5x^2#

#color(white)(aaaaaaaa)##+6x^3-9x^2#

#color(white)(aaaaaaaa)##+0x^3+4x^2+2x#

#color(white)(aaaaaaaaaaaaaa)##+4x^2-6x#

#color(white)(aaaaaaaaaaaaaa)##+0x^2+8x-10#

#color(white)(aaaaaaaaaaaaaaaaaaaa)##+8x-12#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaa)##+2#

The remainder is #=2# and the quotient is #=2x^3+3x^2+2x+4#

#(4x^4+0x^3-5x^2+2x-10)/(2x-3)=(2x^3+3x^2+2x+4)+2/(2x-3)#