Solve -2m^{4}-m^{3}-6m^2+7)-(3m^4-m^3-2m^2-m-9)

$$- 2 m ^ { 4 } - m ^ { 3 } - 6 m ^ { 2 } + 7 ) - ( 3 m ^ { 4 } - m ^ { 3 } - 2 m ^ { 2 } - m - 9 )$$

Factor

$$\left(m+1\right)\left(7-7m+m^{2}-2m^{3}\right)$$

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 7 and q divides the leading coefficient -2. One such root is -1. Factor the polynomial by dividing it by m+1. Polynomial -2m^{3}+m^{2}-7m+7 is not factored since it does not have any rational roots.

$$\left(m+1\right)\left(-2m^{3}+m^{2}-7m+7\right)$$

Evaluate

$$\left(m+1\right)\left(7-7m+m^{2}-2m^{3}\right)$$