Solve (8/3x^3-5/17x^2+9x-2/34)+(7/6x^3+frac{3}{34}x^2+frac{5}{77})

$$( \frac { 8 } { 3 } x ^ { 3 } - \frac { 5 } { 17 } x ^ { 2 } + 9 x - \frac { 2 } { 34 } ) + ( \frac { 7 } { 6 } x ^ { 3 } + \frac { 3 } { 34 } x ^ { 2 } + \frac { 5 } { 77 } )$$

Evaluate

$$\frac{23x^{3}}{6}-\frac{7x^{2}}{34}+9x+\frac{8}{1309}$$

Solution Steps

Reduce the fraction \frac{2}{34} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}x^{3}-\frac{5}{17}x^{2}+9x-\frac{1}{17}+\frac{7}{6}x^{3}+\frac{3}{34}x^{2}+\frac{5}{77}$$

Combine \frac{8}{3}x^{3} and \frac{7}{6}x^{3} to get \frac{23}{6}x^{3}.

$$\frac{23}{6}x^{3}-\frac{5}{17}x^{2}+9x-\frac{1}{17}+\frac{3}{34}x^{2}+\frac{5}{77}$$

Combine -\frac{5}{17}x^{2} and \frac{3}{34}x^{2} to get -\frac{7}{34}x^{2}.

$$\frac{23}{6}x^{3}-\frac{7}{34}x^{2}+9x-\frac{1}{17}+\frac{5}{77}$$

Add -\frac{1}{17} and \frac{5}{77} to get \frac{8}{1309}.

$$\frac{23}{6}x^{3}-\frac{7}{34}x^{2}+9x+\frac{8}{1309}$$

Factor

$$\frac{30107x^{3}-1617x^{2}+70686x+48}{7854}$$

Solution Steps

Factor out \frac{1}{7854}. Polynomial 30107x^{3}-1617x^{2}+70686x+48 is not factored since it does not have any rational roots.

$$\frac{30107x^{3}-1617x^{2}+70686x+48}{7854}$$