Solve g(u)=u^4-2/3u^3-2u^2+2u(-12)

$$g ( u ) = u ^ { 4 } - \frac { 2 } { 3 } u ^ { 3 } - 2 u ^ { 2 } + 2 u ( - 12 )$$

Factor

$$\frac{u\left(3u^{3}-2u^{2}-6u-72\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{3u^{4}-2u^{3}-6u^{2}-72u}{3}$$

Consider 3u^{4}-2u^{3}-6u^{2}-72u. Factor out u.

$$u\left(3u^{3}-2u^{2}-6u-72\right)$$

Rewrite the complete factored expression. Polynomial 3u^{3}-2u^{2}-6u-72 is not factored since it does not have any rational roots.

$$\frac{u\left(3u^{3}-2u^{2}-6u-72\right)}{3}$$

Evaluate

$$u^{4}-\frac{2u^{3}}{3}-2u^{2}-24u$$

Solution Steps

Multiply 2 and -12 to get -24.

$$u^{4}-\frac{2}{3}u^{3}-2u^{2}-24u$$