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

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Answer 1 · 2017-05-04T12:29:56

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

We perform a long division

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

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

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

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

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

Therefore,

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

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