Solve (1/12x^{4}+4/5x^3+5/8x^2+8)+(-7/12x^4+frac{3}{8}x^2-8)

$$( \frac { 1 } { 12 } x ^ { 4 } + \frac { 4 } { 5 } x ^ { 3 } + \frac { 5 } { 8 } x ^ { 2 } + 8 ) + ( - \frac { 7 } { 12 } x ^ { 4 } + \frac { 3 } { 8 } x ^ { 2 } - 8 )$$

Evaluate

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

Solution Steps

Combine \frac{1}{12}x^{4} and -\frac{7}{12}x^{4} to get -\frac{1}{2}x^{4}.

$$-\frac{1}{2}x^{4}+\frac{4}{5}x^{3}+\frac{5}{8}x^{2}+8+\frac{3}{8}x^{2}-8$$

Combine \frac{5}{8}x^{2} and \frac{3}{8}x^{2} to get x^{2}.

$$-\frac{1}{2}x^{4}+\frac{4}{5}x^{3}+x^{2}+8-8$$

Subtract 8 from 8 to get 0.

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

Factor

$$-\frac{1}{2}\left(x-\frac{4-\sqrt{66}}{5}\right)\left(x-\frac{\sqrt{66}+4}{5}\right)x^{2}$$