1 / 17

7-4

7-4. Factoring ax 2 + bx + c. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 1. Holt Algebra 1. Warm Up Find each product. 1. ( x – 2)(2 x + 7) Find each trinomial. 2. x 2 + 4x – 32. ESSENTIAL QUESTION.

credle
Download Presentation

7-4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7-4 Factoring ax2+ bx + c Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

  2. Warm Up Find each product. 1. (x – 2)(2x + 7) Find each trinomial. 2. x2 +4x– 32

  3. ESSENTIAL QUESTION How do you factor quadratic trinomials of the form ax2 + bx + c ?

  4. When you multiply (3x + 2)(2x + 5), the coefficient of the x2-term is the product of the coefficients of the x-terms. Also, the constant term in the trinomial is the product of the constants in the binomials. (3x +2)(2x +5) = 6x2 + 19x +10

  5. (2x + 4)(3x + 1) = 6x2 + 14x + 4   (1x + 4)(6x + 1) = 6x2 + 25x + 4 (3x + 4)(2x + 1) = 6x2 + 11x + 4  (1x + 2)(6x + 2) = 6x2 + 14x + 4  (1x + 1)(6x + 4) = 6x2 + 10x + 4 Example 1: Factoring ax2 + bx + c by Guess and Check Factor 6x2 + 11x + 4 by guess and check. Write two sets of parentheses. ( _ + _ )( _ + _ ) ( x + _)( _ x + _) The coefficient of the x2 term is 6. The constant term in the trinomial is 4. Try factors of 6 for the coefficients and factors of 4 for the constant terms.

  6. (1x + 3)(6x + 1) = 6x2 + 19x + 3  (1x + 1)(6x + 3) = 6x2 + 9x + 3  (2x + 1)(3x + 3) = 6x2 + 9x + 3  (3x + 1)(2x + 3) = 6x2 + 11x + 3 Example 2 Factor each trinomial by guess and check. 6x2 + 11x + 3 ( _ + _ )( _ + _ ) Write two sets of parentheses. ( x + _)( _ x + _) The coefficient of the x2 term is 6. The constant term in the trinomial is 3. Try factors of 6 for the coefficients and factors of 3 for the constant terms.

  7. (1x–1)(3x + 8) = 3x2 + 5x– 8  (1x–2)(3x + 4) = 3x2– 2x– 8  (1x–4)(3x + 2) = 3x2– 10x– 8  (1x–8)(3x + 1) = 3x2– 23x– 8 Example 3 Factor each trinomial by guess and check. 3x2– 2x– 8 ( _ + _ )( _ + _ ) Write two sets of parentheses. ( x + _)( _ x + _) The coefficient of the x2 term is 3. The constant term in the trinomial is –8. Try factors of 3 for the coefficients and factors of 8 for the constant terms.

  8. Factors of 3 Factors of 16Outer+Inner  1 and 3 –1 and –16 1(–16) + 3(–1) = –19  1( – 8) + 3(–2) = –14 1 and 3 – 2 and – 8  – 4 and – 4 1( – 4) + 3(– 4)= –16 1 and 3  = 3x2– 16x + 16 Example 4: Factoring ax2 + bx + c When c is negative 3x2– 16x + 16 ( _ + _ )( _ + _ ) a = 3 and c = 16, Outer + Inner = –16. ( x + _)( _ x + _) (x– 4)(3x– 4) Use the Foil method. Check(x– 4)(3x– 4) = 3x2– 4x– 12x + 16

  9. Factors of 6 Factors of 5Outer+Inner  1 and 5 1(5) + 6(1) = 11 1 and 6  1 and 5 2(5) + 3(1) = 13 2 and 3  1 and 5 3(5) + 2(1) = 17 3 and 2  = 6x2 + 17x + 5 Example 5 6x2 + 17x + 5 ( _ + _ )( _ + _ ) a = 6 and c = 5, Outer + Inner = 17. ( x + _)( _ x + _) Use the Foil method. (3x + 1)(2x + 5) Check(3x + 1)(2x + 5)= 6x2 + 15x + 2x + 5

  10. Factors of 9 Factors of 4Outer+Inner  3(–4) + 3(–1) = –15 3 and 3 –1 and – 4  3(–2) + 3(–2) = –12 3 and 3 – 2 and – 2  – 4 and – 1 3(–1) + 3(– 4)= –15 3 and 3  = 9x2– 15x + 4 Example 6 9x2– 15x + 4 ( _ + _ )( _ + _ ) a = 9 and c = 4, Outer + Inner = –15. ( x + _)( _ x + _) (3x– 4)(3x– 1) Use the Foil method. Check (3x– 4)(3x– 1) = 9x2– 3x– 12x + 4

  11. Factors of 3 Factors of 12Outer+Inner  1 and 3 1 and 12 1(12) + 3(1) = 15  2 and 6 1(6) + 3(2) = 12 1 and 3  3 and 4 1(4) + 3(3) = 13 1 and 3  = 3x2 + 13x + 12 Example 7 3x2 + 13x + 12 a = 3 and c = 12, Outer + Inner = 13. ( _ + _ )( _ + _ ) ( x + _)( _ x + _) (x + 3)(3x + 4) Use the Foil method. Check (x + 3)(3x + 4) = 3x2 + 4x + 9x + 12

  12. Factors of 3 Factors of –4Outer+Inner  1(4) + 3(–1) = 1 1 and 3 –1 and 4  1(2) + 3(–2) = – 4 1 and 3 –2 and 2  –4 and 1 1(1) + 3(–4) = –11 1 and 3  4 and –1 1(–1) + 3(4) = 11 1 and 3  = 3n2 + 11n –4 Example: Factoring ax2 + bx + c When c is Negative 3n2 + 11n– 4 ( _ + _ )( _ + _ ) a = 3 and c = – 4, Outer + Inner = 11 . ( x + _)( _ x + _) (n + 4)(3n– 1) Use the Foil method. Check (n + 4)(3n– 1) = 3n2 –n + 12n –4

  13. 1 and 4 1(4) + 4(–1) = 0 –1 and 4  1(2) + 4(–2) = –6 1 and 4 –2 and2  –4 and1 1(1) + 4(–4) = –15 1 and 4 (x – 4)(4x + 1)  = 4x2– 15x–4 Example: Factoring ax2 + bx + c When b & c are Negative 4x2– 15x– 4 a = 4 and c = –4, Outer + Inner = –15. ( _ + _ )( _ + _ ) ( x + _)( _ x + _) Factors of 4 Factors of – 4Outer+Inner Use the Foil method. Check(x– 4)(4x + 1) = 4x2 + x – 16x–4

  14. Factors of 4 Factors of –3Outer+Inner  1 and 4 1(–3)+ 4(1) = 1 1 and –3  1(3) – 4(1) = – 1 1 and 4 –1 and3 (4n + 3)(n– 1) Example 4n2–n– 3 ( _ + _ )( _ + _ ) a = 4 and c = –3, Outer + Inner = –1. ( x + _)( _ x + _) Use the Foil method. Check (4n + 3)(n– 1) = 4n2– 4n + 3n – 3 = 4n2–n – 3

  15. Factors of -2 Factors of -3Outer+Inner  1 and -2 3 and -1 -1(1) + 3(-2) = -7  1 and -2 1(1)+ -2(-3) = 7 -3 and 1 (x - 3)(-2x + 1) Example: Factoring ax2 + bx + c When a is Negative –2x2 + 7x - 3. (_ x + )(_ x+ ) Now: a = 2 and c = -3; Outer + Inner = 5 ANS: (x - 3)(-2x + 1)

  16. Factors of 6 Factors of 12Outer+Inner  2 and 3 4 and3 2(3) + 3(4) = 18  2 and 3 2(4)+ 3(3) = 17 3 and 4 (2x + 3)(3x + 4) Example –6x2– 17x– 12 ( _ + _ )( _ + _ ) Factor out –1. -1( x + _)( _ x + _) a = 6 and c = 12; Everything positive! –1(6x2 + 17x + 12) –1(2x + 3)(3x + 4)

  17. Lesson Quiz Factor each trinomial. Check your answer. 1. 5x2 + 17x + 6 2. 2x2 + 5x – 12 3. 6x2 – 23x + 7 4. –4x2 + 11x + 20 (5x + 2)(x + 3) (2x– 3)(x + 4) (3x– 1)(2x– 7) (–x + 4)(4x + 5)

More Related