Simplify the rational expression.
-$\frac { 2 m ^ { 3 } - 2 m ^ { 2 } - 12 m } { m ^ { 2 } - 5 m + 6 }$
A) $2 \mathrm {~m}$
B) $\frac { 2 m ( m + 3 ) } { ( m - 3 ) }$
C) $\frac { 2 m ( m + 2 ) } { ( m - 2 ) }$
D) $\frac { 2 m ( m - 3 ) ( m + 2 ) } { ( m + 3 ) ( m - 2 ) }$

Question

Quizplus · Accepted Answer

First, factor both the numerator and the denominator. The numerator $2m^3 - 2m^2 - 12m$ factors into $2m(m^2 - m - 6)$, which further factors into $2m(m-3)(m+2)$. The denominator $m^2 - 5m + 6$ factors into $(m-3)(m-2)$. Simplifying, we get $\frac{2m(m-3)(m+2)}{(m-3)(m-2)}$, which simplifies to $\frac{2m(m+2)}{m-2}$, matching choice C.

Simplify the Rational Expression 2m3−2m2−12mm2−5m+6\frac { 2 m ^ { 3 } - 2 m ^ { 2 } - 12 m } { m ^ { 2 } - 5 m + 6 }m2−5m+62m3−2m2−12m​

Simplify the Rational Expression $\frac { 2 m ^ { 3 } - 2 m ^ { 2 } - 12 m } { m ^ { 2 } - 5 m + 6 }$