How do you divide $\frac{4 a^{4} - 5 a^{2} + 2 a - 10}{2 a - 3}$ $(4a^4 -5a^2 +2a -10 )/(2a- 3)$ ?

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How do you divide $\frac{4 a^{4} - 5 a^{2} + 2 a - 10}{2 a - 3}$ $(4a^4 -5a^2 +2a -10 )/(2a- 3)$ ?

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Answer 1 · 2016-11-01T12:50:47

The answer is $2 a^{3} + 3 a^{2} + 2 a + 4 + \frac{2}{2 a - 3}$ $2a^3+3a^2+2a+4 +2/(2a-3)$

Explanation:

Let's make a long division
$a a a$ $color(white)(aaa)$ $4 a^{4}$ $4a^4$ $a a a a a$ $color(white)(aaaaa)$ $- 5 a^{2} + 2 a - 10$ $-5a^2+2a-10$ $∣$ $∣$ $2 a - 3$ $2a-3$
$a a a$ $color(white)(aaa)$ $4 a^{4} - 6 a^{3}$ $4a^4-6a^3$ $a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ #∣2a^3+3a^2+2a+4#
$a a a a$ $color(white)(aaaa)$ $0 + 6 a^{3} - 5 a^{2}$ $0+6a^3-5a^2$
$a a a a a a$ $color(white)(aaaaaa)$ $+ 6 a^{3} - 9 a^{2}$ $+6a^3-9a^2$
$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $0 + 4 a^{2} + 2 a$ $0+4a^2+2a$
$a a a a a a a a a a a$ $color(white)(aaaaaaaaaaa)$ $+ 4 a^{2} - 6 a$ $+4a^2-6a$
$a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaa)$ $0 + 8 a - 10$ $0+8a-10$
$a a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaaa)$ $8 a - 12$ $8a-12$
$a a a a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaaaaa)$ $0 + 2$ $0+2$

So the answer is $2 a^{3} + 3 a^{2} + 2 a + 4 + \frac{2}{2 a - 3}$ $2a^3+3a^2+2a+4 +2/(2a-3)$

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How do you divide $\frac{4 a^{4} - 5 a^{2} + 2 a - 10}{2 a - 3}$ $(4a^4 -5a^2 +2a -10 )/(2a- 3)$ ?

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Explanation:

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How do you divide $\frac{4 a^{4} - 5 a^{2} + 2 a - 10}{2 a - 3}$ $(4a^4 -5a^2 +2a -10 )/(2a- 3)$ ?