Solve -8x^5+8x^3-2x

$$-8 { x }^{ 5 } +8 { x }^{ 3 } -2x$$

Factor

$$-2x\left(2x^{2}-1\right)^{2}$$

Solution Steps

Factor out 2.

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

Consider -4x^{5}+4x^{3}-x. Factor out x.

$$x\left(-4x^{4}+4x^{2}-1\right)$$

Consider -4x^{4}+4x^{2}-1. Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -4x^{4} and n divides the constant factor -1. One such factor is 2x^{2}-1. Factor the polynomial by dividing it by this factor.

$$\left(2x^{2}-1\right)\left(-2x^{2}+1\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 2x^{2}-1,-2x^{2}+1.

$$2x\left(2x^{2}-1\right)\left(-2x^{2}+1\right)$$

Evaluate

$$-2x\left(2x^{2}-1\right)^{2}$$