Solve 32-m^5

$$32 - m ^ { 5 }$$

Factor

$$\left(m-2\right)\left(-m^{4}-2m^{3}-4m^{2}-8m-16\right)$$

Solution Steps

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 32 and q divides the leading coefficient -1. One such root is 2. Factor the polynomial by dividing it by m-2. Polynomial -m^{4}-2m^{3}-4m^{2}-8m-16 is not factored since it does not have any rational roots.

$$\left(m-2\right)\left(-m^{4}-2m^{3}-4m^{2}-8m-16\right)$$

Evaluate

$$32-m^{5}$$