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

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

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Answer 1 · 2018-08-11T07:32:18

The remainder is $= 2$ $=2$ and the quotient is $= 2 x^{3} + 3 x^{2} + 2 x + 4$ $=2x^3+3x^2+2x+4$

Explanation:

Perform a long division

$a a a a$ $color(white)(aaaa)$ $4 x^{4} + 0 x^{3} - 5 x^{2} + 2 x - 10$ $4x^4+0x^3-5x^2+2x-10$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $2 x - 3$ $2x-3$

$a a a a$ $color(white)(aaaa)$ $4 x^{4} - 6 x^{3}$ $4x^4-6x^3$ $a a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaaa)$ $∣$ $|$ $2 x^{3} + 3 x^{2} + 2 x + 4$ $2x^3+3x^2+2x+4$

$a a a a$ $color(white)(aaaa)$ $0 x^{4} + 6 x^{3} - 5 x^{2}$ $0x^4+6x^3-5x^2$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $+ 6 x^{3} - 9 x^{2}$ $+6x^3-9x^2$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $+ 0 x^{3} + 4 x^{2} + 2 x$ $+0x^3+4x^2+2x$

$a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaa)$ $+ 4 x^{2} - 6 x$ $+4x^2-6x$

$a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaa)$ $+ 0 x^{2} + 8 x - 10$ $+0x^2+8x-10$

$a a a a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaaaaa)$ $+ 8 x - 12$ $+8x-12$

$a a a a a a a a a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaaaaaaaaaa)$ $+ 2$ $+2$

The remainder is $= 2$ $=2$ and the quotient is $= 2 x^{3} + 3 x^{2} + 2 x + 4$ $=2x^3+3x^2+2x+4$

$\frac{4 x^{4} + 0 x^{3} - 5 x^{2} + 2 x - 10}{2 x - 3} = (2 x^{3} + 3 x^{2} + 2 x + 4) + \frac{2}{2 x - 3}$ $(4x^4+0x^3-5x^2+2x-10)/(2x-3)=(2x^3+3x^2+2x+4)+2/(2x-3)$

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

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