How do you divide $\frac{5 m^{3} - 7 m^{2} + 14}{m^{2} - 2}$ $(5m^3 - 7m^2 + 14) / (m^2 - 2)$ ?

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Answer 1 · 2017-05-04T12:29:56

The quotient is $= 5 m - 7$ $=5m-7$ and the remainder is $= 10 m$ $=10m$

We perform a long division

$a a a a$ $color(white)(aaaa)$ $5 m^{3} - 7 m^{2}$ $5m^3-7m^2$ $a a a a a a$ $color(white)(aaaaaa)$ $+ 14$ $+14$ $∣$ $|$ $m^{2} - 2$ $m^2-2$

$a a a a$ $color(white)(aaaa)$ $5 m^{3}$ $5m^3$ $a a a a$ $color(white)(aaaa)$ $- 10 m$ $-10m$ $a a a a a a$ $color(white)(aaaaaa)$ #|5m-7#

$a a a a$ $color(white)(aaaa)$ $0 - 7 m^{2}$ $0-7m^2$ $a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $+ 14$ $+14$

$a a a a a a$ $color(white)(aaaaaa)$ $- 7 m^{2}$ $-7m^2$ $a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $+ 14$ $+14$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $- 0 + 10 m$ $-0+10m$ $a a a a$ $color(white)(aaaa)$ $+ 0$ $+0$

Therefore,

$(5 m^{3} - 7 m^{2} + 14) = (m^{2} - 2) (5 m - 7) + 10 m$ $(5m^3-7m^2+14)=(m^2-2)(5m-7)+10m$

How do you divide 5m3−7m2+14m2−2(5m^3 - 7m^2 + 14) / (m^2 - 2)?