Solve -4w^{2}-w^{3}-w^2w^3-2w^2-6w^3

$$- 4 w ^ { 2 } - w ^ { 3 } - w ^ { 2 } w ^ { 3 } - 2 w ^ { 2 } - 6 w ^ { 3 }$$

Evaluate

$$-w^{2}\left(w^{3}+7w+6\right)$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-4w^{2}-w^{3}-w^{5}-2w^{2}-6w^{3}$$

Combine -4w^{2} and -2w^{2} to get -6w^{2}.

$$-6w^{2}-w^{3}-w^{5}-6w^{3}$$

Combine -w^{3} and -6w^{3} to get -7w^{3}.

$$-6w^{2}-7w^{3}-w^{5}$$

Factor

$$-w^{2}\left(w^{3}+7w+6\right)$$

Solution Steps

Factor out w^{2}. Polynomial -w^{3}-7w-6 is not factored since it does not have any rational roots.

$$w^{2}\left(-6-7w-w^{3}\right)$$