Solve x^3+1/5x+2/2x^2+1/16+1/32

$$x ^ { 3 } + \frac { 1 } { 5 } x + \frac { 2 } { 2 } x ^ { 2 } + \frac { 1 } { 16 } + \frac { 1 } { 32 }$$

Evaluate

$$x^{3}+x^{2}+\frac{x}{5}+\frac{3}{32}$$

Solution Steps

Divide 2 by 2 to get 1.

$$x^{3}+\frac{1}{5}x+1x^{2}+\frac{1}{16}+\frac{1}{32}$$

Add \frac{1}{16} and \frac{1}{32} to get \frac{3}{32}.

$$x^{3}+\frac{1}{5}x+1x^{2}+\frac{3}{32}$$

For any term t, t\times 1=t and 1t=t.

$$x^{3}+\frac{1}{5}x+x^{2}+\frac{3}{32}$$

Factor

$$\frac{160x^{3}+160x^{2}+32x+15}{160}$$

Solution Steps

Factor out \frac{1}{160}. Polynomial 160x^{3}+160x^{2}+32x+15 is not factored since it does not have any rational roots.

$$\frac{160x^{3}+32x+160x^{2}+15}{160}$$