Solve 4x^4-22x^2+18x

$$4 x ^ { 4 } - 22 x ^ { 2 } + 18 x$$

Factor

$$2x\left(x-1\right)\left(2x^{2}+2x-9\right)$$

Solution Steps

Factor out 2.

$$2\left(2x^{4}-11x^{2}+9x\right)$$

Consider 2x^{4}-11x^{2}+9x. Factor out x.

$$x\left(2x^{3}-11x+9\right)$$

Consider 2x^{3}-11x+9. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 9 and q divides the leading coefficient 2. One such root is 1. Factor the polynomial by dividing it by x-1.

$$\left(x-1\right)\left(2x^{2}+2x-9\right)$$

Rewrite the complete factored expression. Polynomial 2x^{2}+2x-9 is not factored since it does not have any rational roots.

$$2x\left(x-1\right)\left(2x^{2}+2x-9\right)$$

Evaluate

$$2x\left(2x^{3}-11x+9\right)$$