1. Standard form of an equation means we write an equation based on its exponents. 1.Arrange the terms so that the largest exponent comes first, then the second largest, and so on. 2.The constant, if there is one, has to go last. Example: becomes Basics of Polynomials Remediation Notes: 1 st 2 nd 3 rd 4 th 5 th

2. The degree of a polynomial can tell us how many possible solutions a function can have. That does not mean that the function has that many, it just means it could have up to that many so if you do not see the same number of solutions as the largest exponent you need to look a little further to make sure you have them all. Here, the largest exponent is 4. This means that this function can have 0, 1, 2, 3 or 4 real solutions. By graphing, and zooming out, you can see that there are only 2 solutions. Basics of Polynomials Remediation Notes:

3. An example of the maximum number of possible solutions of each polynomial is shown below. You will not always have the maximum number in your solutions. Basics of Polynomials Remediation Notes: Highest Exponent: 1 Max Solutions: 1 Highest Exponent: 1 Max Solutions: 1 Highest Exponent: 2 Max Solutions: 2 Highest Exponent: 2 Max Solutions: 2 Highest Exponent: 3 Max Solutions: 3 Highest Exponent: 3 Max Solutions: 3 Highest Exponent: 5 Max Solutions: 5 Highest Exponent: 5 Max Solutions: 5 Highest Exponent: 4 Max Solutions: 4 Highest Exponent: 4 Max Solutions: 4

4. The solutions to a function can also be referred to as the roots, zeros, or x-intercepts. To find the solutions you can: 1.Graph 2.Factor 3.Complete the Square 4.Use the Quadratic Formula When you factor you can identify the multiplicity for a function. Multiplicity is simply the repetition of factors (binomials) for a function. To describe a function using multiplicity: 1.Factor the equation for the function 2.Once you have factored to a set of binomials determine how many of each you have. 3.Find the roots, then identify the multiplicity associates with that root. 4.When you have multiple roots showing in factored form it does NOT mean you have multiple roots in the graph. Basics of Polynomials Remediation Notes:

5. Example: To describe a function using multiplicity: 1.Factor the equation for the function 2.Once you have factored to a set of binomials determine how many of each you have. 3.Find the roots, then identify the multiplicity associates with that root. 4.Write answer in correct form. NOTE: When you have multiple roots showing in factored form it does NOT mean you have multiple roots in the graph. Basics of Polynomials Remediation Notes: Given: Factored form: Organize your binomials: Find solutions/roots: 1123 1, multiplicity of 1 -3, multiplicity of 1 -1, multiplicity of 2 2, multiplicity of 3