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 $=2x^3+3x^2+2x+4$

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

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