Solve 3x^6+6x^4+3x^2=

$$3 x ^ { 6 } + 6 x ^ { 4 } + 3 x ^ { 2 } =$$

Factor

$$3x^{2}\left(x^{2}+1\right)^{2}$$

Solution Steps

Factor out 3.

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

Consider x^{6}+2x^{4}+x^{2}. Factor out x^{2}.

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

Consider x^{4}+2x^{2}+1. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x^{2} and b=1.

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

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

$$3x^{2}\left(x^{2}+1\right)^{2}$$

Evaluate

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