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Algebra 3 Warm-Up 2.2 List the factors of 36 1, 36 2, 18 3, 12 4, 9 6,

Algebra 3 Warm-Up 2.2 List the factors of 36 1, 36 2, 18 3, 12 4, 9 6, . Algebra 3 Lesson 2.2 Objective: SSBAT factor a polynomial by factoring out the GCF and using Difference of Squares. Standards: M11.D.2.2.2. Monomial An expression with 1 term 5x 2 -3mn 3 k 8

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Algebra 3 Warm-Up 2.2 List the factors of 36 1, 36 2, 18 3, 12 4, 9 6,

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  1. Algebra 3 Warm-Up 2.2 List the factors of 36 1, 36 2, 18 3, 12 4, 9 6,

  2. Algebra 3 Lesson 2.2 Objective: SSBAT factor a polynomial by factoring out the GCF and using Difference of Squares. Standards: M11.D.2.2.2

  3. Monomial • An expression with 1 term • 5x2 • -3mn3k • 8 • Binomial • An expression with 2 terms • 4x – 2 • 15x3 + 8y • Trinomial • An expression with 3 terms • 8x5 – 5w3 + 2 • 16 – 3x + 5m4

  4. Factors • The numbers used in a multiplication problem • 5 x 3 = 15, 5 and 3 are the factors of 15 • List the Factors of 24 •  1, 2, 3, 4, 6, 8, 12, 24

  5. Greatest Common Factor (GCF) • The biggest number that is a factor of all of the numbers in a set. • Find the GCF of 18 and 45 • Factors of 18: 1, 2, 3, 6, 9, 18 • Factors of 45: 1, 3, 5, 9, 15, 45 • GCF of 18 and 45 is 9

  6. Finding the GCF of expressions (variables) • Example: 6x4y and 10x2 • Find the GCF of the Coefficients (numbers in front) • Find the GCF of each variable pieceby •  Look at only one set of like variables at a time • If the variable does not appear in all of the terms do not use it in the GCF • If the variable appears in every term use the one with the smaller exponent in the GCF

  7. Find the GCF of each. 1. 25x2y4 and 10x3y  GCF: 5x2y 2. 21mn2k and 10m2n2  mn2

  8. 3. 12x4y, 9x5y2, 21x7yw3  GCF: 3x4y 4. m5n3k2 and mnk  GCF: mnk

  9. Factoring • Rewriting an expression as a multiplication problem • 2 · 5 is the factored form of 10 • 3(x + 4) is the factored form of 3x + 12

  10. Factoring Out the GCF • 1. Find the GCF of all of the terms in the polynomial • Write the GCF outside of the parentheses • Divide each term of the polynomial by the GCF and write this expression inside the parentheses

  11. Examples: Factor out the GCF of each. 2w3 + 10w The GCF is 2w = 2w(w2 + 5)

  12. Examples: Factor out the GCF of each. 18n3 + 9n2 – 24n The GCF is 3n = 3n(6n2 + 3n – 8)

  13. Examples: Factor out the GCF of each. 20x6 – 12x3 + 4x The GCF is 4x = 4x(5x5 – 3x2 + 1)

  14. Examples: Factor out the GCF of each. 4. 15mn3– 9m2n4 + 18m3n5 The GCF is 3mn3 = 3mn3(5 – 3mn + 6m2n2)

  15. Perfect Square • A number that you can take the Square Root of • 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,… • Perfect Square expressions are x2, x4, x6, …

  16. Difference of Squares • An expression of the a2 – b2 • Perfect Square – Perfect Square • Examples: x2– 4 • m2 – 25 • 9x2 – 1 • *** x2 + 4 is NOT a difference of squares because of the PLUS ***

  17. Factoring a Difference of Squares • a2 – b2 = (a + b)(a – b) • Take the square root of each term • Add the 2 square roots in one ( ) • Subtract the 2 square roots in another ( )

  18. Factor each Difference of Squares x2 – 64 = ( + )( – ) 81 – x2 =( + )( – ) 8 8 x x x 9 9 x

  19. Factor each Difference of Squares 3. 4x2 – 25 = ( + )( – ) 4. w2 – y2 = ( + )( – ) 5 5 2x 2x y w w y

  20. Factor each Difference of Squares 5. 49x2 – 1 =( + )( – ) 6. x2 – 130 Can’t Do – It is NOT a Difference of Squares  130 is not a perfect square x2 + 9 Can’t Do – It is NOT a Difference of Squares  It’s Plus not Minus 1 1 7x 7x

  21. w6 – 196 = (w3 + 14)(w3 – 14) 100x22 – y16 = (10x11 – y8)(10x11 + y8)

  22. On Your Own. Factor out the GCF. 8x3 – 20x5+ 2x2 Factor the Difference of Squares. 100 – x2 2x2(4x – 5x3 + 1) (10 + x)(10 – x)

  23. Homework Worksheet 2.2

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