Solve 1/9x^{4}-3/6x^{3}-8/12x^2-3/6x^3+frac{9}{9}x^2+frac{6}{8}x-frac{2}{12}x^2+frac{6}{8}x+frac{4}{16}

$$\frac { 1 } { 9 } x ^ { 4 } - \frac { 3 } { 6 } x ^ { 3 } - \frac { 8 } { 12 } x ^ { 2 } - \frac { 3 } { 6 } x ^ { 3 } + \frac { 9 } { 9 } x ^ { 2 } + \frac { 6 } { 8 } x - \frac { 2 } { 12 } x ^ { 2 } + \frac { 6 } { 8 } x + \frac { 4 } { 16 }$$

Evaluate

$$\frac{x^{4}}{9}-x^{3}+\frac{x^{2}}{6}+\frac{3x}{2}+\frac{1}{4}$$

Solution Steps

Divide 9 by 9 to get 1.

$$\frac{1}{9}x^{4}-\frac{3}{6}x^{3}-\frac{8}{12}x^{2}-\frac{3}{6}x^{3}+1x^{2}+\frac{6}{8}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{9}x^{4}-\frac{1}{2}x^{3}-\frac{8}{12}x^{2}-\frac{3}{6}x^{3}+1x^{2}+\frac{6}{8}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1}{9}x^{4}-\frac{1}{2}x^{3}-\frac{2}{3}x^{2}-\frac{3}{6}x^{3}+1x^{2}+\frac{6}{8}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{9}x^{4}-\frac{1}{2}x^{3}-\frac{2}{3}x^{2}-\frac{1}{2}x^{3}+1x^{2}+\frac{6}{8}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

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

$$\frac{1}{9}x^{4}-x^{3}-\frac{2}{3}x^{2}+1x^{2}+\frac{6}{8}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

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

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{3}x^{2}+\frac{6}{8}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{3}x^{2}+\frac{3}{4}x-\frac{2}{12}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{3}x^{2}+\frac{3}{4}x-\frac{1}{6}x^{2}+\frac{6}{8}x+\frac{4}{16}$$

Combine \frac{1}{3}x^{2} and -\frac{1}{6}x^{2} to get \frac{1}{6}x^{2}.

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{6}x^{2}+\frac{3}{4}x+\frac{6}{8}x+\frac{4}{16}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{6}x^{2}+\frac{3}{4}x+\frac{3}{4}x+\frac{4}{16}$$

Combine \frac{3}{4}x and \frac{3}{4}x to get \frac{3}{2}x.

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{6}x^{2}+\frac{3}{2}x+\frac{4}{16}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{1}{9}x^{4}-x^{3}+\frac{1}{6}x^{2}+\frac{3}{2}x+\frac{1}{4}$$

Factor

$$\frac{4x^{4}-36x^{3}+6x^{2}+54x+9}{36}$$

Solution Steps

Factor out \frac{1}{36}. Polynomial 4x^{4}-36x^{3}+6x^{2}+54x+9 is not factored since it does not have any rational roots.

$$\frac{4x^{4}-18x^{3}-24x^{2}-18x^{3}+36x^{2}+27x-6x^{2}+27x+9}{36}$$