This is the second of two lessons whose purpose is to introduce students to polynomial division, focusing specifically on dividing by linear factors.
In this lesson, students are introduced to polynomial long division, which is similar to long division involving rational numbers, but organized based on the exponent of the variable instead of powers of 10. Similar structures between integers and polynomials are reinforced in this lesson as students compare what long division looks like with each and use the long division to identify factors (MP7).
An optional activity is included in this lesson and should be used if students need extra practice multiplying and dividing polynomials strategically. Students will use long division in their work with rational expressions later in this unit, in particular when they study the end behavior of rational functions.
- Compare and contrast diagrams and long division as ways of representing division.
- Use long division to find the quotient of two polynomials.
- Let’s learn a different way to divide polynomials.
- I can use long division to divide polynomials.
How the outputs of a function change as we look at input values further and further from 0.
This function shows different end behavior in the positive and negative directions. In the positive direction the values get larger and larger. In the negative direction the values get closer and closer to -3.
The power to which a factor occurs in the factored form of a polynomial. For example, in the polynomial \((x-1)^2(x+3)\), the factor \(x-1\) has multiplicity 2 and the factor \(x+3\) has multiplicity 1.