Solve (1/5x^3+2/3x^2-6)+(-4/5x^2+x+7/3x^2)

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

Evaluate

$$\frac{x^{3}}{5}+\frac{11x^{2}}{5}+x-6$$

Solution Steps

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

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

Combine -\frac{2}{15}x^{2} and \frac{7}{3}x^{2} to get \frac{11}{5}x^{2}.

$$\frac{1}{5}x^{3}+\frac{11}{5}x^{2}-6+x$$

Factor

$$\frac{x^{3}+11x^{2}+5x-30}{5}$$

Solution Steps

Factor out \frac{1}{15}.

$$\frac{3x^{3}+10x^{2}-90-12x^{2}+15x+35x^{2}}{15}$$

Consider 3x^{3}+10x^{2}-90-12x^{2}+15x+35x^{2}. Multiply and combine like terms.

$$3x^{3}+33x^{2}+15x-90$$

Consider 3x^{3}+33x^{2}+15x-90. Factor out 3.

$$3\left(x^{3}+11x^{2}+5x-30\right)$$

Rewrite the complete factored expression.

$$\frac{x^{3}+11x^{2}+5x-30}{5}$$