Question: Factor the polynomial. \[ 4m^5 n^4 - 36m^4 n^3 \] Select the correct choice below and, if…

Factor the polynomial.

\[ 4m^5 n^4 - 36m^4 n^3 \]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. \[ 4m^5 n^4 - 36m^4 n^3 = \boxed{\phantom{0}} \]

(Factor completely. Simplify your answer.)

B. The polynomial is prime.

Solution

To factor the polynomial \(4m^5n^4 - 36m^4n^3\), follow these steps: Identify the greatest common factor (GCF) of the terms. The GCF of \(4m^5n^4\) and \(36m^4n^3\) is \(4m^4n^3\). Factor out the GCF from the polynomial: \[ 4m^5n^4 - 36m^4n^3 = 4m^4n^3(mn - 9) \] Thus, the completely factored form of the polynomial is: \[ 4m^4n^3(mn - 9) \]