Solve {l}{2+4}{+2}{-x^4+x}{+3x}{+1/2}

$$\left. \begin{array} { l } { 2 + 4 } \\ { + 2 } \\ { - x ^ { 4 } + x } \\ { + 3 x } \\ { + \frac { 1 } { 2 } } \end{array} \right.$$

Evaluate

$$\frac{17}{2}+4x-x^{4}$$

Solution Steps

Add 2 and 4 to get 6.

$$6+2-x^{4}+x+3x+\frac{1}{2}$$

Add 6 and 2 to get 8.

$$8-x^{4}+x+3x+\frac{1}{2}$$

Combine x and 3x to get 4x.

$$8-x^{4}+4x+\frac{1}{2}$$

Add 8 and \frac{1}{2} to get \frac{17}{2}.

$$\frac{17}{2}-x^{4}+4x$$

Factor

$$\frac{17+8x-2x^{4}}{2}$$

Solution Steps

Factor out \frac{1}{2}. Polynomial -2x^{4}+8x+17 is not factored since it does not have any rational roots.

$$\frac{17-2x^{4}+8x}{2}$$