1 / 19

MTH 10905 Algebra

MTH 10905 Algebra. Factoring Trinomials of the form ax 2 + bx + c where a = 1 Chapter 5 Section 3. Factoring Trinomials. It is important that you understand sections 5.3 and 5.4 to be successful in Chapter 6.

lilika
Download Presentation

MTH 10905 Algebra

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. MTH 10905Algebra Factoring Trinomials of the form ax2 + bx + c where a = 1 Chapter 5 Section 3

  2. Factoring Trinomials • It is important that you understand sections 5.3 and 5.4 to be successful in Chapter 6. • In this section we learn factoring a trinomial in the form of ax2 + bx + c where a = 1; for example, x2 + 5x + 6 • In section 5.4 we learn factoring a trinomial in the form of ax2 + bx + c where a ¹ 1; for example, 2x2 + 7x + 3

  3. Trial and Error • When factoring x2 + bx + c you will always get (x + ) (x + ) • Write down the factors of the constant, c, and try them in the shaded area. • You need the factors of c that sum to b • Use the FOIL method to check

  4. Trinomials in the form ax2 + bx + c, a=1 • It is important that you know what a, b and c equals. • Examples: • x2 + 7x + 12 = (x + 3)(x + 4) FOIL a = 1, b = 7, c = 12 (3)(4) = 12 factors of 12 that sum to 7 3 + 4 = 7 • x2 – 2x – 24 = (x – 6)(x + 4) FOIL a = 1, b = -2, c = -24 (-6)(4) = -24 factors of -24 that sum to -2 (-6)+(4) = -2

  5. Trial and Error Example: x2 + 12x + 20 a=1 b=12 c=20 (x + 2)(x + 10) You can always check using FOIL method (x + 2) (x + 10) (x)(x) + (x)(10)+ (2)(x) + (2)(10) x2 + 10x + 2x + 20 x2 + 12x + 20

  6. Helpful Hint • If b = neg, c = pos, then factor = 2 negative • If b = neg, c = neg, then factor = 1 pos 1 neg • If b = pos, c = neg, then factor = 1 pos 1 neg • If b = pos, c = pos, then factor = 2 positive Example: Using x2 + bx – c , determine the sign of the numbers in the factors: One positive and one negative factor

  7. Factoring Trinomials Example: x2 + x – 72 a=1 b=1 c=-72 (x + 9)(x – 8) Check using FOIL (x + 9) (x – 8) (x)(x) + (x)(-8)+ (9)(x) + (9)(-8) x2 + (-8x) + 9x + (-72) x2 + x – 72

  8. Factoring Trinomials Example: x2 – x – 72 a=1 b=-1 c=-72 (x – 9)(x + 8) Check using FOIL (x – 9)(x + (8) (x)(x) + (x)(8)+ (-9)(x) + (-9)(8) x2 + 8x + (-9x) + (-72) x2 – x – 72

  9. Factoring Trinomials Example: x2 – 11x + 30 a=1 b=-11 c=32 (x – 5)(x – 6) Check using FOIL (x – 5)(x – 6) (x)(x) + (x)(-6)+ (-5)(x) + (-5)(-6) x2 + (-6x) + (-5x) + 30 x2 – 11x + 30

  10. Factoring Trinomials Example: t2 + 4x – 32 a=1 b=4 c=-32 (t – 4)(t + 8) Check using FOIL (t – 4)(t + 8) (t)(t) + (t)(8)+ (-4)(t) + (-4)(8) t2 + (8t) + (-4t) – 32 t2 + 4t – 32

  11. Factoring Trinomials Example: x2 – 14x + 49 a=1 b=-14 c=49 (x – 7)(x – 7) (x – 7)2 Check using FOIL (x – 7)(x – 7) (x)(x) + (x)(-7)+ (-7)(x) + (-7)(-7) x2 + (-14x) + 49 x2 – 14x + 49

  12. Factoring Trinomials Example: x2 – 2x – 63 a=1 b=-2 c=-63 (x – 9)(x + 7) Check using FOIL (x – 9)(x + 7) (x)(x) + (x)(7)+ (-9)(x) + (-9)(7) x2 + 7x + (-9x) – 63 x2 – 2x – 63

  13. Factoring Trinomials Example: x2 + 10x + 20 a=1 b=10 c=20 PRIME A polynomial that cannot be factored using only integer coefficients is called a prime polynomial. No factors of c that can sum to b.

  14. Factoring Trinomials Example: x2 + 4xy + 4y2 a=1 b=4 c=4 (x + 2y)(x + 2y) (x + 2y)2 Check using FOIL (x + 2y)(x + 2y) (x)(x) + (x)(2y)+ (2y)(x) + (2y)(2y) x2 + 2xy + 2xy + 4y2 x2 + 4xy + 4y2 The last term of the factors must contain a y in order to get the y2

  15. Factoring Trinomials Example: x2 – xy – 30y2 a=1 b=1 c=-30 (x – 6y)(x + 5y) The last term of the factors must contain a y in order to get the y2 Check using FOIL (x – 6) (x + 5y) (x)(x) + (x)(5y)+ (-6y)(x) + (-6y)(5y) x2 + 5xy + (-6xy) + (-30y2) x2 – xy – 30y2

  16. Removing a Common Factorfrom a Trinomials Example: 3x2 – 21x + 18 3(x2 – 7x + 6) 3(x – 1)(x – 6) Sometimes each term has a GCF that we must pull out first making it easier to factor. Check using FOIL 3(x – 1)(x – 6) 3[(x)(x) + (x)(-6)+ (-1)(x) + (-1)(-6)] 3[x2 + (-6x) + (-1x) + 6] 3[x2 – 7x + 6] 3x2 – 21x + 18

  17. Removing a Common Factorfrom a Trinomials Example: 3m3 + 9m2 – 84m 3m(m2 + 3m – 28) 3m(m + 7)(m – 4) Check using FOIL 3m(m + 7)(m – 4) 3m[(m)(m) + (m)(7)+ (7)(m) + (7)(-4)] 3m[m2 + 7m + 7m + -28] 3m[m2 + 14m - 28] 3m3 + 9m2 – 84

  18. REMEMBER • Always factor out the GCF first. • A table can be helpful. Use one column for all possible factors of c an another column for the sum of the factors. • One or both factors of c can be negative. • When c is positive, the two factors will have the same sign as b. • When c is negative, the two factors will have opposite signs. • When the factors have opposite signs, the larger of the two will be the same sign as b • You should always check your work by multiplying.

  19. HOMEWORK 5.3 Page 311: #17, 19, 21, 27, 39, 45, 63, 73

More Related