When dealing with a polynomial equation, our first strategy is to try to solve by factoring. If we get all terms to one side, leaving a zero on the other, we can use the zero product property to solve the equation if we can factor. Here’s a video with some examples.
Here is a worksheet where you can use various kinds of factoring to solve equations.
When we have a rational equation, that is an equation where we divide by a polynomial, we turn it into a polynomial equation by multiplying both sides by the denominators (or LCD). In doing so, we have to make sure we don’t multiply both sides by zero. Here’s a video going over an example of that.
Here is a worksheet with more practice solving rational equations.
We use a similar strategy if we have a radical equation, that is one with a radical sign. We solve for the radical and then take both sides to the appropriate power to again turn the equation into a nearly equivalent polynomial equation.
Here’s a worksheet with radical equatoins.