1 / 11

6.3 Adding, Subtracting, & Multiplying Polynomials

6.3 Adding, Subtracting, & Multiplying Polynomials. p. 338. To + or - , + or – the coeff. of like terms! Vertical format :. Add 3x 3 +2x 2 -x-7 and x 3 -10x 2 +8. 3x 3 + 2x 2 – x – 7 + x 3 – 10x 2 + 8 Line up like terms 4x 3 – 8x 2 – x + 1.

leal
Download Presentation

6.3 Adding, Subtracting, & Multiplying Polynomials

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. 6.3 Adding, Subtracting, & Multiplying Polynomials p. 338

  2. To + or - , + or – the coeff. of like terms!Vertical format : • Add 3x3+2x2-x-7 and x3-10x2+8. • 3x3 + 2x2 – x – 7 + x3 – 10x2 + 8 Line up like terms • 4x3 – 8x2 – x + 1

  3. Horizontal format : Combine like terms • (8x3 – 3x2 – 2x + 9) – (2x3 + 6x2 – x + 1)= • (8x3 – 2x3)+(-3x2 – 6x2)+(-2x + x) + (9 – 1)= • 6x3 + -9x2 + -x + 8 = • 6x3 – 9x2 – x + 8

  4. Examples: Adding & Subtracting • (9x3 – 2x + 1) + (5x2 + 12x -4) = • 9x3 + 5x2 – 2x + 12x + 1 – 4 = • 9x3 + 5x2 + 10x – 3 • (2x2 + 3x) – (3x2 + x – 4)= • 2x2 + 3x – 3x2 – x + 4 = • 2x2 - 3x2 + 3x – x + 4 = • -x2 + 2x + 4

  5. Multiplying Polynomials: Vertically • (-x2 + 2x + 4)(x – 3)= • -x2 + 2x + 4 * x – 3 3x2 – 6x – 12 -x3 + 2x2 + 4x -x3 + 5x2 – 2x – 12

  6. Multiplying Polynomials : Horizontally • (x – 3)(3x2 – 2x – 4)= • (x – 3)(3x2) • + (x – 3)(-2x) • + (x – 3)(-4) = • (3x3 – 9x2) + (-2x2 + 6x) + (-4x + 12) = • 3x3 – 9x2 – 2x2 + 6x – 4x +12 = • 3x3 – 11x2 + 2x + 12

  7. Multiplying 3 Binomials : • (x – 1)(x + 4)(x + 3) = • FOIL the first two: • (x2 – x +4x – 4)(x + 3) = • (x2 + 3x – 4)(x + 3) = • Then multiply the trinomial by the binomial • (x2 + 3x – 4)(x) + (x2 + 3x – 4)(3) = • (x3 + 3x2 – 4x) + (3x2 + 9x – 12) = • x3 + 6x2 + 5x - 12

  8. Some binomial products appear so much we need to recognize the patterns! • Sum & Difference (S&D): • (a + b)(a – b) = a2 – b2 • Example: (x + 3)(x – 3) = x2 – 9 • Square of Binomial: • (a + b)2 = a2 + 2ab + b2 • (a - b)2 = a2 – 2ab + b2

  9. Last Pattern • Cube of a Binomial • (a + b)3 = a3 + 3a2b + 3ab2 + b3 • (a – b)3 = a3 - 3a2b + 3ab2 – b3

  10. Example: • (x + 5)3 = a = x and b = 5 x3 + 3(x)2(5) + 3(x)(5)2 + (5)3 = x3 + 15x2 + 75x + 125

  11. Assignment

More Related