Solve {l}{2x^{2}-5+6x^{3}-4x^5}{-5+2x^2+6x^3-4x^5}

$$\left. \begin{array} { l } { 2 x ^ { 2 } - 5 + 6 x ^ { 3 } - 4 x ^ { 5 } } \\ { - 5 + 2 x ^ { 2 } + 6 x ^ { 3 } - 4 x ^ { 5 } } \end{array} \right.$$

Evaluate

$$-8x^{5}+12x^{3}+4x^{2}-10$$

Solution Steps

Subtract 5 from -5 to get -10.

$$2x^{2}-10+6x^{3}-4x^{5}+2x^{2}+6x^{3}-4x^{5}$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$4x^{2}-10+6x^{3}-4x^{5}+6x^{3}-4x^{5}$$

Combine 6x^{3} and 6x^{3} to get 12x^{3}.

$$4x^{2}-10+12x^{3}-4x^{5}-4x^{5}$$

Combine -4x^{5} and -4x^{5} to get -8x^{5}.

$$4x^{2}-10+12x^{3}-8x^{5}$$

Factor

$$2\left(-4x^{5}+6x^{3}+2x^{2}-5\right)$$

Solution Steps

Multiply and combine like terms.

$$-8x^{5}+12x^{3}+4x^{2}-10$$

Factor out 2. Polynomial -4x^{5}+6x^{3}+2x^{2}-5 is not factored since it does not have any rational roots.

$$2\left(-4x^{5}+6x^{3}+2x^{2}-5\right)$$