ALG2.MATH.7.E
Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping.
Algebra II · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
linear factorquadratic factorpolynomial expressiondegree threedegree foursum of cubesdifference of cubesfactoringfactoring by grouping
Skills
- factor (sum of cubes) #dok2
- factor (difference of cubes) #dok2
- factor (polynomial expressions of degree three and four by grouping) #dok2
- determine (linear factors of a polynomial expression) #dok2
- determine (quadratic factors of a polynomial expression) #dok2
Learning Targets
- I can factor the sum of two cubes in a polynomial expression of degree three or four. #dok2
- I can factor the difference of two cubes in a polynomial expression of degree three or four. #dok2
- I can factor a polynomial of degree three or four by grouping. #dok2
- I can identify linear and quadratic factors in higher degree polynomials. #dok2
- I can explain why factoring methods are chosen for different types of polynomials. #dok3
- I can justify my choices and results when factoring complex polynomial expressions. #dok3
Big Ideas
- Complex polynomial expressions of degree three and four can be simplified and solved by identifying and extracting their linear and quadratic factors through established algebraic methods.
- Understanding and applying specialized factoring techniques—including the sum and difference of cubes and factoring by grouping—enables students to break down higher-degree polynomials into simpler, solvable components.
Essential Questions
- How do you recognize when a polynomial expression can be factored using the sum or difference of cubes?
- Why is it important to find both linear and quadratic factors when factoring higher degree polynomials?
- What strategies can be used to factor a polynomial of degree three or four by grouping?
- How do you know your set of factors is complete and correct?
- In what real-world contexts might factoring polynomials of higher degree be useful?