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Comprehensive Guide to Simplifying Expressions and Factoring Polynomials

This comprehensive guide focuses on simplifying expressions, finding the greatest common factor (GCF) of monomials, and factoring polynomials including trinomials. Learn step-by-step methods to factor using the GCF and grouping techniques. The guide emphasizes critical strategies, including working with two-term and three-term polynomials, tackling the difference of squares, and using sum and difference of cubes for efficient factoring. Ideal for students looking to strengthen their algebra skills with clear examples and practice drills.

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Comprehensive Guide to Simplifying Expressions and Factoring Polynomials

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  1. Drill #25 Simplify each expression.

  2. Drill #26 Find the GCF of the following monomials: Factor each polynomial using the GCF:

  3. Drill #27 Factor each polynomial using the GCF: Factor by Grouping Factor the following trinomials:

  4. Drill #28 Factor each polynomial using the GCF: Factor the following trinomials:

  5. Drill #52 Factor each polynomial :

  6. Drill #53 Factor each polynomial :

  7. Drill #54 Factor each polynomial :

  8. GCF: Monomials To find the GCF of two monomials: • Find the GCF of the coefficients • For each common, the GCF is the common variable with the lower degree • Combine the GCF of the coefficients and the variables together to make one term

  9. GCF Examples: 8-1 Study Guide (even problems) Classwork: 8 – 16 (EVEN)

  10. Factor Polynomials: GCF To factor polynomials: • Find the GCF of all terms in the polynmial • Use the distributive property to undistribute GCF • Factor the remaining expression (if possible)

  11. Factor Polynomials: Factor by Grouping To factor a polynomial by grouping (4 or 6 terms) • GCF Factor the first two (three) terms • GCF factor the last two (three) terms • If there is a common factor between them, factor it (undistribute) Ex: 6ax + 3ay + 2bx + by

  12. Factoring Polynomials* Always GCF factor 1st!!!!!!! 1. GCF Factoring 2. Two Terms: - Difference of Squares - Difference of Cubes - Sum of Cubes 3. Three Terms: Trinomial Factoring 4. Four or More Terms Factor by Grouping

  13. Multiply binomials: What is ( x + 2) (x + 5)?

  14. Trinomial Factoring: Three Terms* Factoring: Where m + n = b and m(n) = c To factor trinomials make a factor sum table!

  15. Trinomial Factoring Examples* Example 1a, b: 8-3 Study Guide Classwork: 2-8 (even)

  16. Factoring Trinomials with 2 2nd Degree Terms Example:#20

  17. Trinomial Factoring: Three Terms*: Factor by Grouping Method Factoring: 1. GCF factor (if possible) 2. Find factors m,n of a*c (that add up to b) 3. Change bxto mx + nx 4. Factor by grouping Ex: To factor trinomials make a factor sum table!

  18. Trinomial Factoring: Three Terms*: Illegal Method Factoring: 1. GCF factor (if possible) 2. Multiply ac and rewrite as 3. Factor to (x + m)(x + n) 4. Divide m and n by a and reduce fractions 5. The denom. of any fractions that don’t reduce become coefficients To factor trinomials make a factor sum table!

  19. Trinomial Factoring Examples* Example 1, 2:8-4 Study Guide Classwork: 8-4 Study Guide#2 – 8 (even)

  20. FOIL the following binomials What is (x – 4 )(x + 4)

  21. Two Terms: Factoring Difference of Squares* To factor difference of squares: Examples:

  22. Two Terms: Factoring Sum of Cubes* To factor sum of cubes: Example:

  23. Two Terms: Factoring Difference of Cubes* To factor difference of cubes: Examples:

  24. Classwork: 6-5 Study Guide #1 – 9 All

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