Question

What is the factorization of the polynomial below? x^3-4x^2+45x

Answer 1

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Answer 2

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).