1 / 17

Factoring

Factoring. Learning Goal. I will be able to factor trinomials using factoring by grouping. Special Products. For any numbers a and b: Difference of Squares: a 2 – b 2 = (a + b)(a – b) General Trinomial: acx 2 + (ad + bc)x + bd = (ax + b)(cx + d)

patty
Download Presentation

Factoring

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. Factoring

  2. Learning Goal I will be able to factor trinomials using factoring by grouping.

  3. Special Products For any numbers a and b: Difference of Squares: a2 – b2 = (a + b)(a – b) General Trinomial: acx2 + (ad + bc)x + bd = (ax + b)(cx + d) Perfect Square Trinomial: a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2

  4. Factoring By Grouping… Find the factors of step #2 which add up to equal the middle term. (bx) Check for the greatest common factor (GCF). Multiply the first term by the last term. (ax2)(c) = ? Substitute the factors from step #3 into the original trinomial, replacing the middle term. (Make bx two terms) Group the four term polynomial from step #4. (Make 2 binomials.) Factor by Grouping. If a polynomial is unfactorable, it is considered prime.

  5. Factor Completely. If the polynomial is not factorable, write prime. 1. xy – 2x + y2 – 2y 2. x2 + 10x + 9 (xy – 2x) + (y2 – 2y) x(y – 2) + y(y – 2) (y – 2) (x + y) x2 + 9x + x + 9 (x2 + 9x) + (x + 9) x(x + 9) + 1(x + 9) (x + 9) (x + 1)

  6. Factor Completely. If the polynomial is not factorable, write prime. 3. 6x2 + 27x - 15 4. 2x2 – 11x + 12 3[2x2 + 9x – 5] 3[2x2 + 10x – x – 5] 3[(2x2 + 10x) + (-x – 5)] 3[2x(x + 5) – 1(x + 5)] 3(x + 5) (2x – 1) 2x2 – 8x – 3x + 12 (2x2 – 8x) + (-3x + 12) 2x(x – 4) – 3(x – 4) (x – 4) (2x – 3)

  7. Factor Completely. If the polynomial is not factorable, write prime. 5. 3x2 – 17x - 6 6. 6x2 + x – 12 3x2 – 18x + x - 6 (3x2 – 18) + (x – 6) 3x(x – 6) + 1(x – 6) (x – 6) (3x + 1) 6x2 + 9x – 8x – 12 (6x2 + 9x) + (-8x – 12) 3x(2x + 3) – 4(2x + 3) (2x + 3) (3x – 4)

  8. ( + )( - ) y y Factor Completely. If the polynomial is not factorable, write prime. 7. y2 - 9 8. 16x2 + 25y2 y2 – 0y – 9 y2 – 3y + 3y – 9 (y2 – 3y) + (3y – 9) y(y – 3) + 3(y – 3) (y – 3) (y + 3) A Sum of Squares cannot be factored. OR… y2 – 9 (y)2 – (3)2 (y + 3)(y – 3)

  9. Factor Completely. If the polynomial is not factorable, write prime. 9. 2x4 - 2 10. 7mx2 + 2x2n – 7my2 – 2ny2 2(x4 – 1) 2(x2 + 1)(x2 – 1) 2(x2 + 1) (x + 1)(x – 1) (7mx2 + 2x2n) + (-7my2 – 2ny2) x2(7m + 2n) – y2(7m + 2n) (7m + 2n) (x2 – y2) (7m + 2n) (x – y)(x + y)

  10. 4 4 4 Given the perimeter of a square is (12x2 + 32) inches, what is the length of one side in terms of x? P = 4s 12x2 + 32 = 4s 3x2 + 8 = s The length of one side is (3x2 + 8) inches.

  11. The area of a pool is x2 + 8x + 15 yards2. Find the dimensions of the pool in terms of x. A = LW LW = x2 + 8x + 15 LW = x2 + 5x + 3x + 15 LW = (x2 + 5x) + (3x + 15) LW = x(x + 5) + 3(x + 5) LW = (x + 5) (x + 3) The dimensions of the pool are (x + 5) yards by (x + 3) yards.

  12. The area of a triangle is found to be 6x2 + 10x + 4 feet2. Find the height and length of the base for this triangle in terms of x. A = ½bh ½bh = 6x2 + 10x + 4 (2) ½bh = (6x2 + 10x + 4)(2) bh = 12x2 + 20x + 8 bh = 12x2 + 12x + 8x + 8 bh = (12x2 + 12x) + (8x + 8) bh = 12x(x + 1) + 8(x + 1) bh = (x + 1) (12x + 8) The length of the base and the height of the triangle are (x + 1) feet and (12x + 8) feet.

  13. The area of the playground at the new park is 12x2 – 17x + 6 yards2. In order for the parks and recreation committee to put a flower bed along the sides of the park they will need to know the dimensions of the playground. The playground at the new park has dimensions of (4x – 3) yards and (3x – 2) yards. A = LW LW = 12x2 – 17x + 6 LW = 12x2 – 9x – 8x + 6 LW = (12x2 – 9x) + (-8x + 6) LW = 3x(4x – 3) – 2(4x – 3) LW = (4x – 3) (3x – 2)

  14. Betty is trying to wrap her sister’s birthday present. The volume of the box that the present is contained in is 16x4 – 81 units3. What are the dimensions of the box? V = LWH LWH = 16x4 – 81 LWH = (4x2 + 9)(4x2 – 9) LWH = (4x2 + 9) (2x + 3)(2x – 3) The dimensions of the box are (4x2 + 9) units by (2x + 3) units by (2x – 3) units.

  15. x x x x Bobby is looking to put a pool in his backyard. He wants to put a uniform sidewalk around the pool that has a width of x. The area of the space where the pool will go is 12x2 + 57x + 63 feet2. What are the dimensions of the pool without the sidewalk? A = LW LW = 12x2 + 57x + 63 LW = 12x2 + 21x + 36x + 63 LW = (12x2 + 21x) + (36x + 63) LW = 3x(4x + 7) + 9(4x + 7) LW = (4x + 7) (3x + 9) Length of pool: 4x + 7 – 2x = 2x + 7 Width of pool: 3x + 9 – 2x = x + 9 The dimensions of the pool are (2x + 7) feet by (x + 9) feet.

  16. What Did I Learn Today?

  17. Homework Factoring Polynomials WS

More Related