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Math 71A

This resource explains the concepts of Greatest Common Factors (GCF) and factoring by grouping, both essential techniques in algebra. The Greatest Common Factor (GCF) of a polynomial is determined by multiplying the lowest powers of common variables. Factoring by grouping involves grouping terms to extract a common factor and simplify the expression. Step-by-step examples illustrate how to identify GCFs and apply grouping methods to effectively factor polynomials. Enhance your understanding of these fundamental algebraic techniques and their applications.

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Math 71A

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  1. Math 71A 5.3 – Greatest Common Factors and Factoring by Grouping

  2. _________________ is the reverse process of multiplication. Multiplication: Factoring: Multiplication: Factoring:

  3. _________________ is the reverse process of multiplication. Multiplication: Factoring: Multiplication: Factoring: Factoring

  4. _________________ is the reverse process of multiplication. Multiplication: Factoring: Multiplication: Factoring: Factoring

  5. _________________ is the reverse process of multiplication. Multiplication: Factoring: Multiplication: Factoring: Factoring

  6. _________________ is the reverse process of multiplication. Multiplication: Factoring: Multiplication: Factoring: Factoring

  7. _________________ is the reverse process of multiplication. Multiplication: Factoring: Multiplication: Factoring: Factoring

  8. Greatest Common Factor (GCF) GCF of a polynomial: ______of the coefficients times each variable to the ___________power. ex: What is the GCF of ? ________

  9. Greatest Common Factor (GCF) GCF of a polynomial: ______of the coefficients times each variable to the ___________power. ex: What is the GCF of ? ________ GCF

  10. Greatest Common Factor (GCF) GCF of a polynomial: ______of the coefficients times each variable to the ___________power. ex: What is the GCF of ? ________ GCF smallest

  11. Greatest Common Factor (GCF) GCF of a polynomial: ______of the coefficients times each variable to the ___________power. ex: What is the GCF of ? ________ GCF smallest

  12. Greatest Common Factor (GCF) GCF of a polynomial: ______of the coefficients times each variable to the ___________power. ex: What is the GCF of ? ________ GCF smallest

  13. Greatest Common Factor (GCF) Ex 1.Factor: Ex 2.Factor: 3 Ex 3.Factor:

  14. Factoring by Grouping Ex 4.Factor: Ex 5.Factor by grouping:

  15. Factoring by Grouping 1. ________ terms that have common monomial factor. 2. ______________ common monomial factor from each group. 3. ______________ remaining common binomial factor.

  16. Factoring by Grouping 1. ________ terms that have common monomial factor. 2. ______________ common monomial factor from each group. 3. ______________ remaining common binomial factor. Group

  17. Factoring by Grouping 1. ________ terms that have common monomial factor. 2. ______________ common monomial factor from each group. 3. ______________ remaining common binomial factor. Group Factor out

  18. Factoring by Grouping 1. ________ terms that have common monomial factor. 2. ______________ common monomial factor from each group. 3. ______________ remaining common binomial factor. Group Factor out Factor out

  19. Factoring by Grouping Ex 6.Factor by grouping:

  20. Factoring by Grouping Note: Sometimes need to rearrange terms to get method to work. Ex 7.Factor by grouping:

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