IM 2.7 - Using Factors and Zeros

Lesson Narrative The purpose of this lesson is for students to use what they have learned about the relationship between the factors of a polynomial and the zeros of a polynomial. Students first use their knowledge of the structure of polynomials in factored form (MP7) to identify an appropriate horizontal range for the graphing windows for polynomials given an equation, and then write a possible equation for a polynomial with specific horizontal intercepts, turning around the work they have done previously. Students also revisit the kind of vertical scaling they encountered in the previous lesson to find an appropriate vertical range for a graphing window. The work students do in this lesson helps them learn how to apply the connections they have been making between graphs and equations.   An important takeaway of this lesson is that a polynomial with a factor of  has a zero when . Students will continue to use this idea throughout future lessons as they build up to the Remainder Theorem, which allows us to prove that a polynomial with a zero at  must have  as a linear factor.

By Algebra two