1 / 12

A.3 Polynomials and Factoring

A.3 Polynomials and Factoring. In the following polynomial, what is the degree and leading coefficient? 4x 2 - 5x 7 - 2 + 3x . Degree = Leading coef. =. 7 -5. Ex. 1 Adding polynomials. (7x 4 - x 2 - 4x + 2) - (3x 4 - 4x 2 + 3x). First, dist. the neg.

latif
Download Presentation

A.3 Polynomials and 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. A.3 Polynomials and Factoring In the following polynomial, what is the degree and leading coefficient? 4x2 - 5x7 - 2 + 3x Degree = Leading coef. = 7 -5 Ex. 1 Adding polynomials (7x4 - x2 - 4x + 2) - (3x4 - 4x2 + 3x) First, dist. the neg. = 4x4 + 3x2 - 7x + 2

  2. Ex. 2 Foil (3x - 2)(5x + 7) = 15x2 + 11x - 14 Ex. 3 The product of Two Trinomials (x + y - 2)(x + y + 2) = x2 + xy + 2x + xy + y2 + 2y -2x - 2y - 4 = x2 + 2xy + y2 - 4

  3. Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 (a + b)0 (a + b)1 (a + b)2 (a + b)3 (a + b)4 (a + b)5 (a + b)6 Pascal’s Triangle can be used to expand polynomials that look like....

  4. Ex. 4 Expand (x + y)3 The row that matches up with this example is row 4. It is 1 3 3 1 These are the coef. in front of each term. 1 3 3 1 1x3y0 + 3x2y1 + 3x1y2 + 1x0y3 Notice that the sum of the exponents always add up to three.

  5. Let’s do (a + b)5 What line of coef. are we going to use? 1 5 10 10 5 1 a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

  6. One more… (2x - 3y)4 Write down the coef. first. 1 4 6 4 1 a4 + 4a3b + 6a2b2 + 4ab3 + b4 Now let a = 2x and b = -3y (2x)4 + 4(2x)3(-3y) + 6(2x)2(-3y)2 + 4(2x)(-3y)3 + (-3y)4 16x4 - 96x3y + 216x2y2 - 216xy3 + 81y4 Day 1

  7. Removing Common Factors Ex. 5 6x3 - 4x = 2x(3x2 - 2) (x - 2)(2x) + (x - 2)(3) = (x - 2)(2x + 3) 3 - 12x2 = 3(1 - 4x2) = 3(1 - 2x)(1 + 2x)

  8. Factoring the Difference of Two Squares Ex. 6 (x + 2)2 - y2 = 16x4 - 81 = (x + 2 - y)(x + 2 + y) or (x - y + 2)(x + y + 2) (4x2 - 9)(4x2 + 9) (2x + 3)(2x - 3)(4x2 + 9) Factoring Perfect Trinomials (4x + 1)(4x + 1) Ex. 7 16x2 + 8x + 1 = = (4x + 1)2

  9. Ex. 8 Factor x2 - 7x + 12 2x2 + x - 15 (x - 3)(x - 4) (2x - 5)(x + 3) Factoring the Sum and Difference of Cubes

  10. Ex. 9 x3 - 27 = (x)3 - (3)3 Let u = x and v = 3 Plug these into the diff. of cubes equation

  11. Ex. 10 Factor 3x3 + 192 First, factor out a 3. 3(x3 + 64) Next, write each term as something cubed and set them equal to a and b. 3((x)3 + (4)3) Let a = x and b = 4

  12. Ex. 11 Factoring by Grouping x3 - 2x2 - 3x + 6 What can we factor out of the first two terms? And the second two terms? { { x2(x - 2) - 3(x - 2) Did you remember to factor a negative from the +6? Now what does each group have in common? Now factor it out. (x - 2)(x2 - 3)

More Related