Solving Polynomial Equations

We want to find the zeros of the polynomial function and write it in standard form. Let's do these things one at a time.

Finding the Zeros

To find the zeros of the given function, we will start by substituting $0$ for $f(x).$ $$\begin{array}{c}f(x)=(x+3)(x-4)(x-3)\\ \Downarrow \\ 0=(x+3)(x-4)(x-3)\end{array}$$ Since the right-hand side of the above equation is written in factored form, we can solve it using the Zero Product Property. The zeros of the function are $x=\text{-}3,$ $x=4,$ and $x=3.$

Writing the Function in Standard Form

To write the function in standard form, we will use the Distributive Property.