The Polynomial identities exercise appears under the Algebra II Math Mission and Mathematics III Math Mission. This exercise explores the idea of an identity, specifically in polynomial expressions.
Types of Problems[]
There are two types of problems in this exercise:
- Find the faulty step in the proof (if there is one): This problem provides a proof of a polynomial identity. The student is asked to determine where there is an error in the reasoning, or say that the proof is valid.
Find the faulty step in the proof (if there is one)
- Select all valid identities: This problem has a list of several possible polynomial identities. The student is asked to select all of the equations from the multiple select list that are true.
Select all valid identities
Strategies[]
Knowledge of many of the factoring and simplification formulas for quadratic expressions (and higher) are encouraged to ensure success on this exercise.
- There are many methods to factor quadratic expressions where the leading coefficient is not one.
- The completion of the square algorithm shows up often on these problems.
- The difference of squares form occurs on these problems.
- One way to ensure accuracy is to expand both sides of any identity and "collect like terms."
- It is technically invalid to work with both sides of an identity when trying to establish it in a proof.
Real-life Applications[]
- An ability to manipulate expressions is used in the calculus to make formulas easier to perform calculus on.
- Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.