Solve 3x^3-9x+6

$$3 x ^ { 3 } - 9 x + 6$$

Factor

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

Solution Steps

Factor out 3.

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

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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