Factoring by Decomposition and Solution Verification

Factoring by Decomposition

• Used when factoring polynomials where the leading coefficient is not $1$.

• Decomposition is standard in the Alberta curriculum, contrasting with BC practice.

• Always inspect the expression after initial factoring to check for additional factoring opportunities, such as a difference of squares.

Practice Exercises and Answer Key Notes

• Example 1 consists of parts a, b, c, and d to be completed collaboratively before independent practice.

• The solutions provided in the answer key for parts b and c are incorrect.

Questions & Discussion

• Question: How can answers to factoring problems always be checked?

• Response: Multiply the factored terms back together to verify they reproduce the original polynomial.