The method of factorization is used to find the roots of a given polynomial. Roots are the solutions of the function. Graphically, these roots are where the curve passes the x-axis. The first step to do is to find the common factor of the equation. That would be x. So you place it outside of the parenthesis.
x³-4x²+45x = x(x² - 4x + 45)
If you solve the quadratic equation inside the parenthesis using the quadratic formula, the roots are imaginary. Therefore, the quadratic equation is already a prime polynomial.
The final answer is x(x² - 4x + 45).