Solve 2x^5+11x^3-63x

$$2 x ^ { 5 } + 11 x ^ { 3 } - 63 x$$

Factor

$$x\left(2x^{2}-7\right)\left(x^{2}+9\right)$$

Solution Steps

Factor out x.

$$x\left(2x^{4}+11x^{2}-63\right)$$

Consider 2x^{4}+11x^{2}-63. Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 2x^{4} and n divides the constant factor -63. One such factor is 2x^{2}-7. Factor the polynomial by dividing it by this factor.

$$\left(2x^{2}-7\right)\left(x^{2}+9\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 2x^{2}-7,x^{2}+9.

$$x\left(2x^{2}-7\right)\left(x^{2}+9\right)$$

Evaluate

$$x\left(2x^{2}-7\right)\left(x^{2}+9\right)$$