Solve 3x^7-27x=

$$3 x ^ { 7 } - 27 x =$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(x^{7}-9x\right)$$

Consider x^{7}-9x. Factor out x.

$$x\left(x^{6}-9\right)$$

Consider x^{6}-9. Rewrite x^{6}-9 as \left(x^{3}\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: x^{3}-3,x^{3}+3.

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

Evaluate

$$3x\left(x^{6}-9\right)$$