Prove polynomial identities

The  exercise appears under the Algebra II Math Mission. This exercise practices determining whether given polynomial identities are true, and whether given proofs of such identities are valid.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the invalid step in the proof: This problem provides the proof of a polynomial identity. The student is expected to find where there is an error in the reasoning. There may not be any invalid steps in the proof. Prove polynomial identities.PNG
 * 2) Select the valid identities: This problem has a list of possible polynomial identities. Student are expected to select all the equations from the multiple choice list that are true. Prove polynomial identities2.PNG

Strategies
Knowledge of many of the factoring and simplification formulas for quadratic expressions (and higher) are encouraged to ensure success on this exercise.
 * 1) An identity is an equation which is true for all values of all its variables.
 * 2) If an equation is not true for even a single value of any variable, then the equation is not an identity.
 * 3) Students can check that an equation is an identity by using properties of operations to rewrite it in a form where both sides are identical.

Real-life Applications

 * 1) Polynomials can be used via power series to represent many complicated functions and calculus is simpler to perform on polynomials than other functions. Thus any comfort with polynomials should increase calculus ability.
 * 2) Factoring polynomials is an important skill in solving inequalities and equations with polynomials.
 * 3) Factoring polynomials can be used for solving equations with polynomials, such as those that appear in many business models.