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Special Cases of Factoring

Chapter 5.5. Special Cases of Factoring. Perfect Square Trinomials. (a + b) 2. a 2 + 2ab + b 2. =. a 2 – 2ab + b 2. =. ( a – b) 2. Perfect Square Trinomials. 1. Check each term to see if there is a GCF of all terms. 2 . Determine if the 1 st and 3 rd terms are perfect squares.

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Special Cases of Factoring

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  1. Chapter 5.5 Special Cases of Factoring Perfect Square Trinomials (a + b)2 a2+ 2ab + b2 = a2– 2ab + b2 = (a – b)2

  2. Perfect Square Trinomials 1. Check each term to see if there is a GCF of all terms. 2. Determine if the 1st and 3rd terms are perfect squares. 3. Determine if the 2ndterm is double the product of the values whose squares are the 1st and 3rdterms. 4. Write as a sum or difference squared. (a + b)2 a2+ 2ab + b2 = a2– 2ab + b2 = (a – b)2

  3. 0 5. Factor. + 25 x + 10 1 x2 1. GCF = 2. Are the 1st and 3rd terms perfect squares (x + 5)2 (x)2 x2= √ 25 = (5)2 3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms √ 10x 2(x)(5) = 4. Write as a sum squared.

  4. 0 6. Factor. + 9 x – 30 1 25x2 1. GCF = 2. Are the 1st and 3rd terms perfect squares (5x – 3)2 (5x)2 25x2 = √ 9 = (-3)2 3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms Used -3 because the second term is – 30x √ -30x 2(5x)(-3) = 4. Write as a difference squared.

  5. 0 7a. Factor. + 36y2 xy + 60 1 25x2 1. GCF = 2. Are the 1st and 3rd terms perfect squares (5x + 6y)2 (5x)2 25x2 = √ 36y2 = (6y)2 3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms √ 60xy 2(5x)(6y) = 4. Write as a sum squared.

  6. 0 7b. Factor. + 9 x3 – 48 1 64x6 1. GCF = 2. Are the 1st and 3rd terms perfect squares (8x3– 3)2 (8x3)2 64x6 = √ 9 = (-3)2 3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms Used -3 because the second term is – 48x3 √ -48x3 2(8x3)(-3) = 4. Write as a difference squared.

  7. 0 8. Factor. + 4 x + 15 1 9x2 1. GCF = 2. Are the 1st and 3rd terms perfect squares Not a perfect square trinomial (3x)2 9x2 = Use trial and error or the grouping method √ 4 = (2)2 3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms 12x 2(3x)(2) = 12x ≠ 15x

  8. 0 8. Factor. 1. GCF = 1 9 x2 + 15 x + 4 2. Grouping Number. (9)(4) = 36 9x2+ 3x + 12x + 4 3. Find 2 integers whose product is 36 and sum is 15. 1, 36 2, 18 3, 12 4. Split into 2 terms.

  9. 0 8. Factor. 5. Factor by grouping. 9 x2 + 15 x + 4 GCF = 3x 9x2 + 3x + 12x + 4 GCF = 4 GCF = (3x + 1) 4 3x + 1 ) ( 3x + 4 ) + 1 ( 3x 3x (3x + 1) (3x + 1) (3x + 1)( ) + 4 3x

  10. 0 10. Factor. + 12 x – 60 3 75x2 GCF = 2. Are the 1st and 3rd terms perfect squares + 4 x – 20 25x2 3( ) (5x)2 25x2 = √ 3(5x – 2)2 4 = (-2)2 3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms Used -2 because the second term is – 20x √ -20x 2(5x)(-2) = 4. Write as a difference squared.

  11. Chapter 5.5 Special Cases of Factoring

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