Solve x^4-3x^4+16x

$$x ^ { 4 } - 3 x ^ { 4 } + 16 x$$

Factor

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

Solution Steps

Factor out x.

$$x\left(x^{3}-3x^{3}+16\right)$$

Consider x^{3}-3x^{3}+16. Multiply and combine like terms.

$$-2x^{3}+16$$

Consider -2x^{3}+16. Factor out 2.

$$2\left(-x^{3}+8\right)$$

Consider -x^{3}+8. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 8 and q divides the leading coefficient -1. One such root is 2. Factor the polynomial by dividing it by x-2.

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

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

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

Evaluate

$$16x-2x^{4}$$

Solution Steps

Combine x^{4} and -3x^{4} to get -2x^{4}.

$$-2x^{4}+16x$$