Explain, in words, the steps to finding all zeros of a polynomial.

1. Synthetic division
2. Simple diamond or dimond grouping
3. set your answer to zero
Idk if thats all the steps

Finding all zeros of a polynomial involves a few steps. Here is a detailed explanation of the process:

1. Start with the polynomial equation: A polynomial equation is an equation of the form f(x) = 0, where f(x) is a polynomial function. To find the zeros, we need to set the equation equal to zero.

2. Synthetic Division: One approach to finding the zeros is through synthetic division, which is particularly helpful when you have a potential zero value to test. Begin by determining the possible zeros using factors of the constant term (the number without any variable terms). Then, use synthetic division to test these values and see if they result in a remainder of zero. If a remainder of zero is obtained, this means the value tested is a zero of the polynomial.

3. Simple Diamond or Diamond Grouping: Another method to find zeros is by using the Simple Diamond or Diamond Grouping approach. Start by grouping the terms of the polynomial in pairs, either horizontally or vertically. Then, factor out any common factors from each pair. By this process, you may uncover additional factors of the polynomial, which could be zeros.

4. Set the Answer to Zero: Once you have obtained a value that satisfies the equation f(x) = 0, set that answer to zero and solve for x. This will give you the specific values of x where the polynomial is equal to zero.

It's important to note that these steps should be followed in order, as they build upon each other to find all the zeros of a polynomial. Also, keep in mind that some polynomials might have multiple zeros, and finding them all can sometimes be a complex process.