Overview
On this page, we review how we can immediately solve a polynomial equation if we are able to factor it completely.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand and apply the zero product property to solve a factored polynomial equation with zero on the right-hand side.
- Solve a given polynomial equation with zero on the right-hand side by factoring the left-hand side completely.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Solve a given polynomial equation by moving terms around so that the right-hand side is zero, then simplifying and factoring the left-hand side.
To prepare for class
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Watch the following video (by Tyler Wallace) which explains the zero product property (which is a property of the real numbers), which states that a product is zero if and only if one of its factors is zero, and how we can use this to solve (factored) polynomial equations where the right-hand side is zero:
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Watch the following video (by Tyler Wallace) which shows how to first factor a polynomial equation before then using the zero product property to determine the solutions:
After class
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Watch the following videos (by Tyler Wallace) which show how a given equation first might have to be rewritten and simplified before solving it by factoring:
