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

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

Evaluate

$$-\frac{5x^{4}}{3}+x^{3}-x^{2}+\frac{x}{4}-2$$

Solution Steps

Combine \frac{1}{3}x^{4} and -2x^{4} to get -\frac{5}{3}x^{4}.

$$-\frac{5}{3}x^{4}+x^{3}-\frac{1}{2}x^{2}-\frac{3}{4}x+1-\frac{1}{2}x^{2}+x-3$$

Combine -\frac{1}{2}x^{2} and -\frac{1}{2}x^{2} to get -x^{2}.

$$-\frac{5}{3}x^{4}+x^{3}-x^{2}-\frac{3}{4}x+1+x-3$$

Combine -\frac{3}{4}x and x to get \frac{1}{4}x.

$$-\frac{5}{3}x^{4}+x^{3}-x^{2}+\frac{1}{4}x+1-3$$

Subtract 3 from 1 to get -2.

$$-\frac{5}{3}x^{4}+x^{3}-x^{2}+\frac{1}{4}x-2$$

Factor

$$\frac{-20x^{4}+12x^{3}-12x^{2}+3x-24}{12}$$

Solution Steps

Factor out \frac{1}{12}. Polynomial -20x^{4}+12x^{3}-12x^{2}+3x-24 is not factored since it does not have any rational roots.

$$\frac{-20x^{4}+12x^{3}-12x^{2}+3x-24}{12}$$