Factor, using the given factor. Assume all variables represent positive real numbers.
-$2 m ^ { 5 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }$
A) $3 m ^ { - 1 / 4 } \left( 2 m ^ { 7 / 4 } - 1 \right)$
B) $m ^ { - 1 / 2 } \left( 2 m ^ { 7 / 4 } - 3 \right)$
C) $m ^ { - 1 / 2 } \left( 2 m ^ { 5 / 4 } + 3 \right)$
D) $m ^ { - 1 / 2 } \left( 6 m ^ { 7 / 4 } - 2 \right)$

Question

Quizplus · Accepted Answer

To factor the given expression $2 m ^ { 5 / 4 } - 3 m ^ { - 1 / 2 }$ using the given factor $m ^ { - 1 / 2 }$, we factor out $m ^ { - 1 / 2 }$ from each term. This gives us $m ^ { - 1 / 2 } \left( 2 m ^ { 5 / 4 + 1 / 2 } - 3 \right)$, which simplifies to $m ^ { - 1 / 2 } \left( 2 m ^ { 7 / 4 } - 3 \right)$.

Factor, Using the Given Factor 2m5/4−3m−1/2;m−1/22 m ^ { 5 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }2m5/4−3m−1/2;m−1/2

Factor, Using the Given Factor $2 m ^ { 5 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }$