Solve x^3-15x^2+63x-81

$$x ^ { 3 } - 15 x ^ { 2 } + 63 x - 81$$

Factor

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

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 -81 and q divides the leading coefficient 1. One such root is 9. Factor the polynomial by dividing it by x-9.

$$\left(x-9\right)\left(x^{2}-6x+9\right)$$

Consider x^{2}-6x+9. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x and b=3.

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

Rewrite the complete factored expression.

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

Evaluate

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