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

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

Evaluate

$$3x^{4}+\frac{x^{3}}{3}-\frac{10x^{2}}{3}-2x+9$$

Solution Steps

Add 5 and 4 to get 9.

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

Combine -\frac{5}{2}x^{2} and -\frac{5}{6}x^{2} to get -\frac{10}{3}x^{2}.

$$3x^{4}-2x+9+\frac{1}{3}x^{3}-\frac{10}{3}x^{2}$$

Factor

$$\frac{9x^{4}+x^{3}-10x^{2}-6x+27}{3}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{18x^{4}-12x+54+2x^{3}-20x^{2}}{6}$$

Consider 18x^{4}-12x+30+2x^{3}-15x^{2}+24-5x^{2}. Multiply and combine like terms.

$$18x^{4}+2x^{3}-20x^{2}-12x+54$$

Consider 18x^{4}+2x^{3}-20x^{2}-12x+54. Factor out 2.

$$2\left(9x^{4}+x^{3}-10x^{2}-6x+27\right)$$

Rewrite the complete factored expression.

$$\frac{9x^{4}+x^{3}-10x^{2}-6x+27}{3}$$