Solve lambda^3-3lambda+2

$$\lambda ^ { 3 } - 3 \lambda + 2$$

Factor

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

Solution Steps

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 \lambda +2.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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