Solve 3/2x^3+4/3x^2-7/5x+1/7+frac{9}{4}x^3-frac{4}{5}x^2-frac{6}{7}x-5

$$\frac{ 3 }{ 2 } { x }^{ 3 } + \frac{ 4 }{ 3 } { x }^{ 2 } - \frac{ 7 }{ 5 } x+ \frac{ 1 }{ 7 } + \frac{ 9 }{ 4 } { x }^{ 3 } - \frac{ 4 }{ 5 } { x }^{ 2 } - \frac{ 6 }{ 7 } x-5$$

Evaluate

$$\frac{15x^{3}}{4}+\frac{8x^{2}}{15}-\frac{79x}{35}-\frac{34}{7}$$

Solution Steps

Combine \frac{3}{2}x^{3} and \frac{9}{4}x^{3} to get \frac{15}{4}x^{3}.

$$\frac{15}{4}x^{3}+\frac{4}{3}x^{2}-\frac{7}{5}x+\frac{1}{7}-\frac{4}{5}x^{2}-\frac{6}{7}x-5$$

Combine \frac{4}{3}x^{2} and -\frac{4}{5}x^{2} to get \frac{8}{15}x^{2}.

$$\frac{15}{4}x^{3}+\frac{8}{15}x^{2}-\frac{7}{5}x+\frac{1}{7}-\frac{6}{7}x-5$$

Combine -\frac{7}{5}x and -\frac{6}{7}x to get -\frac{79}{35}x.

$$\frac{15}{4}x^{3}+\frac{8}{15}x^{2}-\frac{79}{35}x+\frac{1}{7}-5$$

Subtract 5 from \frac{1}{7} to get -\frac{34}{7}.

$$\frac{15}{4}x^{3}+\frac{8}{15}x^{2}-\frac{79}{35}x-\frac{34}{7}$$

Factor

$$\frac{1575x^{3}+224x^{2}-948x-2040}{420}$$

Solution Steps

Factor out \frac{1}{420}. Polynomial 1575x^{3}+224x^{2}-948x-2040 is not factored since it does not have any rational roots.

$$\frac{1575x^{3}+224x^{2}-948x-2040}{420}$$