1 / 17

Adding and Subtracting Polynomials By: Anna Smoak

Adding and Subtracting Polynomials By: Anna Smoak. Warm Up. Definition (in your own words). Facts/Characteristics. A number, a variable, or a product of a number and one or more variables with whole number exponents.

wyoming-bean
Télécharger la présentation

Adding and Subtracting Polynomials By: Anna Smoak

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. Adding and Subtracting PolynomialsBy: Anna Smoak

  2. Warm Up Definition (in your own words) Facts/Characteristics A number, a variable, or a product of a number and one or more variables with whole number exponents No negative exponents (no exponents in the denominator), no addition or subtraction Monomials 3x2y xyz -1 x1/2 a-2 y-2 x + y + z -5x4 12 y ½ b2 Examples Non-examples

  3. Monomials • What does the root word mono- mean? • A monomial contain one term. • Binomials • What does the root word bi- mean? • If monomials contain only one term how many terms do you think a binomial will contain? Example: x2+ 2x NON-Example: x • Trinomial • What does the root word tri- mean? • If a monomial contains one term and a binomial contains two terms how many terms do you think a trinomial will contain? Example: 4x - 6y + 8 NON-Example: x - y ONE TWO THREE

  4. Polynomials • What does the root word poly- mean? • How many terms do you think a polynomial will contain? • A polynomial is a monomial or the sum of monomials • Examples:x2+ 2x,   3x3+ x² + 5x + 6,       4x - 6y + 8 • The ending of these words "nomial" is Greek for "part". • Why is xyx a monomial while x + y + z is a trinomial? xyz is a product of 3 variables with real valued exponents x + y + z is the sum of three monomials MANY

  5. Adding Polynomials • How can we represent x2+ 2x + 2using Algebra Tiles? • How can we represent 2x2+ 2xusing Algebra Tiles? • Represent the sum of x2+ 2x + 2and2x2+ 2xusing Algebra Tiles X2 X X 1 + + 1 X2 X2 X X +

  6. x2+ 2x + 2 + 2x2+ 2x X2 X X 1 X2 X2 X X + + + + 1 X2 X2 X2 X X X X 1 + + + + 1 X2 X2 X2 X X X X 1 + + 1 3x2+ 4x + 2

  7. Adding Polynomials • How can we represent -x2+ x + 5using Algebra Tiles? • How can we represent x2+ 2x - 2 using Algebra Tiles? • Draw a picture that represents how we can find the sum of -x2+ x + 5andx2+ 2x - 2 using Algebra Tiles? - X2 X 1 1 1 + + 1 1 X2 X X 1 - + 1

  8. -x2+ x + 5 + x2+ 2x-2 - X2 X 1 1 1 X2 X X 1 - + + + + 1 1 1 - X2 X2 X X X 1 1 1 1 - + + + + 1 1 1 X X X 1 1 + 1 3x+ 3

  9. How can we find the sum of x2 + 2x + 3 and 3x + 1? • Can you think of any other ways we can add polynomials? Combine Like Terms Simplify x2 + 5x + 4 (x2 + 2x + 3) + (3x + 1) = x2 + 2x + 3x + 3 + 1 = What property allows us to get ride of our parentheses?

  10. What is my first step in simplifying the expression – (x + 1) ? – (x + 1) = – x – 1 What property did we use to simplify the expression?

  11. Subtracting Polynomials • How can we represent -(x2+ x + 5)using Algebra Tiles? • Is there anything that we have to do before we can use the Algebra Tiles? • We must distribute the negative sign -(x2+ x + 5) = - x2- x - 5 = • How can we represent (-2x2+ x - 3)using Algebra Tiles? - X2 X 1 1 1 - - 1 1 - X2 X2 X 1 1 - + 1

  12. Subtracting Polynomials • If (- x2- x - 5) = And (-2x2+ x - 3)= How can we find the DIFFERENCE of (- x2- x - 5) and (-2x2+ x - 3)? (- x2- x - 5) - (-2x2+ x - 3)= (- x2- x - 5) + (2x2- x + 3)= which we can now represent with Algebra Tiles - X2 X 1 1 1 - - 1 1 - X2 X2 X 1 1 - + 1

  13. -x2- x - 5 + 2x2- x + 3 - X2 - X - 1 1 1 X2 X2 - X 1 1 + + 1 1 1 X2 X2 X2 - X - X - 1 1 1 1 1 - + + 1 1 1 X2 X X 1 - - 1 x2- 2x - 2

  14. (3x2 – 5x + 3) – (2x2 – x – 4) Simplify Work Steps (3x2 – 5x + 3) – (2x2 – x – 4) = 3x2 – 5x + 3 – 2x2 + x + 4 = 3x2 – 2x2– 5x + x + 3 + 4 = x2– 4x + 7 Distribute The Negative Sign Combine Like Terms Simplify

  15. Find the difference of (– 2x3 + 5x2 – 4x + 8) and (– 2x3 + 3x – 4) (– 2x3 + 5x2 – 4x + 8) - (– 2x3 + 3x – 4) = (– 2x3 + 5x2 – 4x + 8) + ( 2x3 - 3x + 4) = 5x2 – 7x + 12

  16. Write an expression for the perimeter of the rectangle. Then simplify the expression. Perimeter = length + length + width + width Perimeter = (3x + 1) + (3x + 1) + (x + 2) + (x + 2) Combining Like Terms: Perimeter = (3x + 3x + x + x) + (1 + 1 + 2 + 2) Simplifying : Perimeter = 8x + 6

  17. Ticket out of the door • When two binomials are added, will the sum always, sometimes, or never be a binomial? Explain your answer and give examples to support your answer.

More Related