polynomials
Download
Skip this Video
Download Presentation
Polynomials

Loading in 2 Seconds...

play fullscreen
1 / 23

Polynomials - PowerPoint PPT Presentation


  • 103 Views
  • Uploaded on

Polynomials. Lesson 3.3 Factoring. Polynomials. A math equation consisting of one to many terms. Examples: 6, x , 6x, -1/2xy , 2y + x, x 2 – 5x - 9 Polynomials cannot have a variable as a denominator nor negative exponents. Are the following polynomials? 7/a ¼ xy – 10

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Polynomials' - martina


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
polynomials

Polynomials

Lesson 3.3 Factoring

polynomials2
Polynomials
  • A math equation consisting of one to many terms.
  • Examples:
  • 6, x, 6x, -1/2xy, 2y + x, x2 – 5x - 9
  • Polynomials cannot have a variable as a denominator nor negative exponents.
slide3

Are the following polynomials?

  • 7/a
  • ¼ xy – 10
  • 3pq1/2
  • √7 x4 – x3
  • 8-2
slide4

Polynomials with

  • one term are called monomials
  • 5x3, 8, x2, etc
  • two terms are called binomials
  • 3x – 1, 2x2 + 8, etc
  • three terms are called trinomials
  • 2x2 – 4x + 9
slide5

Variables – a letter that represents one or more numbers

  • 4y = y is the variable
  • Coefficient – number in front of a variable
  • 4y = coefficient is 4
degrees of a polynomial
Degrees of a polynomial
  • The degree of a polynomial is the degree of the term with the highest exponent.
  • Constant term: term without a variable.
slide7

2x – 1 = degree of 1 Constant term of -1 These are called a linear.

  • 2x2 + 8 = degree of 2 Constant term of 8 These are called quadratic.
  • 2x3 – 5 = degree of 3 Constant term of -5 These are called cubic.
example 1
Example 1
  • State the degree, coefficient’s and constant term of the polynomial.
  • 5x3 + x2 – 7x + 9
example 2
Example 2
  • State the degree, coefficient and constant term of the polynomial.
  • 6a – 4a2 - 3
adding and subtracting polynomials
Adding and Subtracting polynomials
  • Find like terms and combine them in order to simplify polynomials.
  • 4x – 2x2 + 3 – 6x2 + 5 – x
try the following
Try the following
  • a2b – ab2 + 4a3b – 7ab2 + 5a2b
  • (3a – 4b + c) + (3b – 5c – 3a)
be careful with subtraction
Be Careful with subtraction
  • (4x2 – 9x + 6) – (2x2 – 3x – 1)
factoring linear polynomials
Factoring Linear polynomials
  • Just as natural numbers can be factored so can polynomials.
  • Find the GCF in each term and then factor.
factoring examples
Factoring Examples
  • 4m + 12
  • GCF = 4
  • = 4 (m + 3)
slide16

6 – 15a

  • GCF = 3
  • = 3 (2 – 5a)
try the following17
Try the following
  • 6n + 9 =
  • 6c + 4c2 =
  • 3g + 6 =
  • 8d + 12d2 =
factoring trinomials
Factoring Trinomials
  • ax2 + bx + c
  • 5 – 10z – 5z2
  • Find the GCF of all three terms.
  • In this example the GCF is 5.
  • Factor out a 5 from each and write as a product.
  • 5 ( 1 – 2z – z2)
examples
Examples
  • 18a2 – 12a + 6
  • 9 + 27x – 45x2
factoring with more than one variable
Factoring with more than one variable
  • Find all GCF’s, numbers and letters.
  • -12 x3y – 20xy2 – 16x2y2
  • GCF for numbers = 4
  • GCF for letters = 1x and 1y
  • 4xy (-3x2 – 5y – 4xy)
ad