Solve 2x-32x^5

$$2 x - 32 x ^ { 5 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x-16x^{5}\right)$$

Consider x-16x^{5}. Factor out x.

$$x\left(1-16x^{4}\right)$$

Consider 1-16x^{4}. Rewrite 1-16x^{4} as 1^{2}-\left(4x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

Consider -4x^{2}+1. Rewrite -4x^{2}+1 as 1^{2}-\left(2x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-2x\right)\left(1+2x\right)$$

Reorder the terms.

$$\left(-2x+1\right)\left(2x+1\right)$$

Rewrite the complete factored expression. Polynomial 4x^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

$$2x-32x^{5}$$