4-4 FACTORING QUADRATICEXPRESSIONSChapter 4 Quadratic Functions and Equations©Tentinger
ESSENTIAL UNDERSTANDING ANDOBJECTIVES   Essential Understanding: you can factor many    quadratic trinomials into product...
IOWA CORE CURRICULUM Algebra A.SSE.2. Use the structure of an expression to  identify ways to rewrite it.
   What are factors?   What are the factors of 12?   Factors of an expression are expressions that have    a product eq...
DISTRIBUTIVE METHOD:   (x + 4)(x + 2)
FOIL METHOD F: first; O: Outer; I: Inner; L: last (x + 4)(x + 2)
FACTORING   To factor, think of FOIL in reverse   Factor x2 + 6x + 8   What factors of 8 add to be 6?   Factoring ax2 ...
MORE FACTORING   x2 + 14x + 40   x2 – 11x +30   - x2 + 14x +32
GCF   Greatest Common Factor (GCF) of an expression   A common factor of the terms in the expression.   Common factor w...
WHAT IS THE EXPRESSION IN FACTOREDFORM?   9 n2 + 9n – 18   4 x2 + 8x + 12
FACTORING AX2 + BX + C            WHEN A    ≠±1AND THE GCF = 1 Find factors of a times c (ac) that add to be b 2x2 + 11x...
PERFECT SQUARE TRINOMIAL A trinomial that is a square of a binomial Example: x2 + 10x + 25 = (x + 5)2 Forms a2 + 2abx ...
DIFFERENCE OF TWO SQUARES   a2 – b2 = (a + b)(a - b) Factor the following 1. 25x2 – 49   2. 16x2 – 81
HOMEWORK Pg. 221 – 222 # 15 – 78 (3s) (22 problems)
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Alg II Unit 4-4 Factoring Quadratic Expressions

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Alg II Unit 4-4 Factoring Quadratic Expressions

  1. 1. 4-4 FACTORING QUADRATICEXPRESSIONSChapter 4 Quadratic Functions and Equations©Tentinger
  2. 2. ESSENTIAL UNDERSTANDING ANDOBJECTIVES Essential Understanding: you can factor many quadratic trinomials into products of two binomials Objectives: Students will be able to:  Find common and binomial factors of quadratic expressions  Factor special quadratics  Perfect square trinomial  Difference of two squares
  3. 3. IOWA CORE CURRICULUM Algebra A.SSE.2. Use the structure of an expression to identify ways to rewrite it.
  4. 4.  What are factors? What are the factors of 12? Factors of an expression are expressions that have a product equal to the given expression Factoring: rewriting an expression as a product of its factors You can use the Distributive Property or the FOIL method to multiply two binomials.
  5. 5. DISTRIBUTIVE METHOD: (x + 4)(x + 2)
  6. 6. FOIL METHOD F: first; O: Outer; I: Inner; L: last (x + 4)(x + 2)
  7. 7. FACTORING To factor, think of FOIL in reverse Factor x2 + 6x + 8 What factors of 8 add to be 6? Factoring ax2 + bx + c when a = ± 1 x2 + 9x + 20 x2 + 14x – 72 - x2 + 13x – 12
  8. 8. MORE FACTORING x2 + 14x + 40 x2 – 11x +30 - x2 + 14x +32
  9. 9. GCF Greatest Common Factor (GCF) of an expression A common factor of the terms in the expression. Common factor with the great coefficient and the greatest exponent Finding Common Factors What is the expression in factored form? 6 x2 + 9x 4 x2 + 20x – 56 7 n2 – 21
  10. 10. WHAT IS THE EXPRESSION IN FACTOREDFORM? 9 n2 + 9n – 18 4 x2 + 8x + 12
  11. 11. FACTORING AX2 + BX + C WHEN A ≠±1AND THE GCF = 1 Find factors of a times c (ac) that add to be b 2x2 + 11x + 12 4x2 – 4x – 3 4x2 + 7x + 3 2x2 – 7x + 6
  12. 12. PERFECT SQUARE TRINOMIAL A trinomial that is a square of a binomial Example: x2 + 10x + 25 = (x + 5)2 Forms a2 + 2abx + b2 = (a + b)2 a2 - 2abx + b2 = (a - b)2 Factor the following 1. 4x2 – 24x + 36 2. 64x2– 16x + 1
  13. 13. DIFFERENCE OF TWO SQUARES a2 – b2 = (a + b)(a - b) Factor the following 1. 25x2 – 49 2. 16x2 – 81
  14. 14. HOMEWORK Pg. 221 – 222 # 15 – 78 (3s) (22 problems)

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