Solve 5/6x^4-4/3x^3-1/3x^2+1/3x^2+3{x}^2-5x+frac{1}{2}+frac{3}{10}-2

$$\frac{ 5 }{ 6 } { x }^{ 4 } - \frac{ 4 }{ 3 } { x }^{ 3 } - \frac{ 1 }{ 3 } { x }^{ 2 } + \frac{ 1 }{ 3 } { x }^{ 2 } +3 { x }^{ 2 } -5x+ \frac{ 1 }{ 2 } + \frac{ 3 }{ 10 } -2$$

Evaluate

$$\frac{5x^{4}}{6}-\frac{4x^{3}}{3}+3x^{2}-5x-\frac{6}{5}$$

Solution Steps

Combine -\frac{1}{3}x^{2} and \frac{1}{3}x^{2} to get 0.

$$\frac{5}{6}x^{4}-\frac{4}{3}x^{3}+3x^{2}-5x+\frac{1}{2}+\frac{3}{10}-2$$

Add \frac{1}{2} and \frac{3}{10} to get \frac{4}{5}.

$$\frac{5}{6}x^{4}-\frac{4}{3}x^{3}+3x^{2}-5x+\frac{4}{5}-2$$

Subtract 2 from \frac{4}{5} to get -\frac{6}{5}.

$$\frac{5}{6}x^{4}-\frac{4}{3}x^{3}+3x^{2}-5x-\frac{6}{5}$$

Factor

$$\frac{25x^{4}-40x^{3}+90x^{2}-150x-36}{30}$$

Solution Steps

Factor out \frac{1}{30}. Polynomial 25x^{4}-40x^{3}+90x^{2}-150x-36 is not factored since it does not have any rational roots.

$$\frac{25x^{4}-40x^{3}+90x^{2}-150x-36}{30}$$