wilcoxj
Uploaded by
26 SLIDES
348 VUES
260LIKES

Polynomials in Algebra 1: Degrees, Adding, and Subtracting

DESCRIPTION

Learn the basics of polynomials in Algebra 1, including monomials, binomials, and trinomials. Understand how to find degrees of terms, add and subtract polynomials, and simplify expressions.

1 / 26

Télécharger la présentation

Polynomials in Algebra 1: Degrees, Adding, and Subtracting

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. Problems of the DaySimplify each expression below. 1. = y13 = -10d7 2. = – 72a33b14 3.

  2. Problems of the DaySimplify each expression below. 4.)5.)6.)

  3. Algebra 1 ~ Chapter 8.4 Polynomials

  4. Remember: A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents. “Mono” – single term The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.

  5. A. 4p4q3 Ex. 1 - Find the degree of each monomial. Add the exponents of the variables: 4 + 3 = 7. The degree is 7. B. 7ed A variable written without an exponent has an exponent of 1. 1+ 1 = 2. The degree is 2. C. 3 There is no variable, but you can write 3 as 3x0. The degree is 0.

  6. * A polynomial is the sum or difference of monomials. The degree of a polynomial is the degree of the term with the greatest degree. “poly” – many An example of a polynomial is 3a + 4b – 8c That expression consists of three monomials “combined” with addition or subtraction.

  7. Some polynomials have special names based on the number of terms they have.

  8. Ex. 2 – Find the degree of each polynomials. Then name the polynomials based on # of terms. A.) 5m4 + 3m B.) -4x3y2 + 3x2 + 5 C.) 3a + 7ab – 2a2b This polynomial has 2 terms, so it is a binomial. The greatest degree is 4, so the degree of the polynomial is 4. This polynomial has 3 terms, so it is a trinomial. The degree of the polynomial is 5. The degree of the polynomial is 3. This polynomial has 3 terms, so it is a trinomial.

  9. Writing Polynomials in Order • The terms of a polynomial are usually arranged so that the powers of one variable are in ascending (increasing) order or descending (decreasing) order.

  10. 6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9 2 Degree 1 5 2 5 1 0 0 Ex. 3 – Arrange the terms of the polynomial so that the powers of x are in descending order. 6x – 7x5 + 4x2 + 9 Find the degree of each term. Then arrange them in decreasing order: The polynomial written in descending order is -7x5 + 4x2 + 6x + 9.

  11. y2 + y6 – 3y y6 + y2 – 3y Ex. 4 - Write the terms of the polynomial so that the powers of x are in descending order. y2 + y6 − 3y Find the degree of each term. Then arrange them in decreasing order: Degree 2 6 1 6 2 1 The polynomial written in descending order is y6 + y2 – 3y.

  12. Algebra 1 ~ Chapter 8.5 “Adding and Subtracting Polynomials”

  13. Warm Up - Simplify each expression by combining like terms. 1.4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n2 5. 3x2 + 6x2 6. 12xy – 4xy 6x 10y 3p Not like terms 9x2 8xy

  14. Just as you can perform operations on numbers, you can perform operations on polynomials. • To add or subtract polynomials, combine like terms.

  15. Example 1: Adding and Subtracting Monomials A. 12p3 + 11p2 + 8p3 Arrange the terms so the “like” terms are next to each other and then simplify. 12p3 + 8p3 + 11p2 20p3 + 11p2 B. 5x2 – 6 – 3x + 8 5x2 – 3x+ 8 – 6 5x2 – 3x + 2

  16. 5x2+ 4x+ 1 + 2x2+ 5x+ 2 Polynomials can be added in either vertical or horizontal form. Simplify (5x2 + 4x + 1) + (2x2 + 5x + 2) In vertical form, align the like terms and add: 7x2+ 9x+ 3

  17. In horizontal form, regroup and combine like terms. (5x2 + 4x + 1) + (2x2 + 5x + 2) = (5x2 + 2x2) + (4x + 5x) + (1 + 2) = 7x2+ 9x+ 3

  18. Example 2: Adding Polynomials A. (4m2 + 5m + 1) + (m2 + 3m + 6) (4m2+ 5m + 1) + (m2+3m+ 6) (4m2+m2) + (5m + 3m)+ (1 + 6) 5m2 + 8m + 7 B. (10xy + x) + (–3xy + y) (10xy + x) + (–3xy + y) (10xy– 3xy) + x +y 7xy+ x +y

  19. Example 2: Adding Polynomials C.

  20. Subtracting Polynomials Simplify (4x + 5) – ( 2x + 1) Option #1: Option #2: Recall that you can subtract a number by adding its opposite. (4x – 2x) + (5 – 1 ) 2x + 4 (4x + 5) + (-2x – 1) (4x + -2x) + (5 + -1) 2x + 4

  21. Example 3: Subtracting Polynomials A. (4m2 + 5m + 1) − (m2 + 3m + 6) (4m2+ 5m + 1) − (m2+3m+ 6) (4m2−m2) + (5m−3m)+ (1 − 6) 3m2 + 2m – 5 B. (10x3 + 5x + 6) − (–3x3 + 4) (10x3 - - 3x3) + (5x – 0x) + (6 – 4) 13x3 + 5x + 2

  22. Example 3C: Subtracting Polynomials (7m4 – 2m2) – (5m4 – 5m2 + 8) (7m4 – 5m4)+ (−2m2 – −5m2) +(0 – 8) (7m4 – 5m4) + (–2m2 + 5m2)– 8 2m4 + 3m2 – 8

  23. Example 3D: Subtracting Polynomials (–10x2 – 3x + 7) – (x2 – 9) (–10x2 – x2) + (−3x – 0x) + (7 – -9) –11x2 – 3x + 16

  24. Lesson Wrap Up Simplify each expression. 1. 7m2 + 3m + 4m2 2. (r2 + s2) – (5r2 + 4s2) 3. (10pq + 3p) + (2pq – 5p + 6pq) 4. (14d2 – 8) – (6d2 – 2d + 1) 11m2 + 3m –4r2 – 3s2 18pq – 2p 8d2 +2d – 9 5. (2.5ab + 14b) – (–1.5ab + 4b) 4ab + 10b

  25. Assignment • Study Guide 8-4 (In-Class) • Study Guide 8-5 (In-Class) • Skills Practice 8-4 (Homework) • Skills Practice 8-5 (Homework)

More Related