Students extend their understanding of polynomial division to abstract situations that involve division by 𝑥 − 𝑎 and by 𝑥 + 𝑎. Through this work they derive the fundamental identities for the difference of two squares and the sum and difference of two cubes. Further, they connect this work back to divisibility of integers.
This lesson bridges the first five lessons of Topic A of this module with the upcoming lessons in Topic B in which students extend work with division and polynomial identities to factoring. In those lessons, they learn the usefulness of the factored form of a polynomial expression to solve polynomial equations and analyze the zeros of the graph of a polynomial function.
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