Classifying Polynomials

1. CLASSIFYING ALGEBRAIC EXPRESSIONS

2. REVIEW/DRILL: Translate the given Algebraic Expression to English Phrase. 6m – 5 x + y + z 3( ab )

3. REVIEW/DRILL: Translate the given Algebraic Expression to English Phrase. 5m 2n 3x + y

4. REVIEW/DRILL: Translate the given Algebraic Expression to English Phrase. 25 + ab 3 (m + n) _1 _x 4

5. “mono” “bi” “tri” “poly” Define:

6. Define the word “ mono ” CLUE:

7. Define the word “ bi ” CLUE:

8. Define the word “ tri ” CLUE:

9. Define the word “ poly ” CLUE:

10. POLYNOMIAL an algebraic expression that represents a sum of ONE or MORE TERMS containing whole number exponents on the variables

11. Remember the parts of a term?

12. NUMERICAL COEFFICIENT The number in an algebraic term.

13. LITERAL COEFFICIENT A letter used to represent a number

14. EXAMPLES: 4 x Numerical coefficient Literal coefficient 45 abc Numerical coefficient Literal coefficient

15. Examples: 3xy 2x + y x 2 – 2x + 6 2x 3 - x 2 + 4x - 10

16. NOT A POLYNOMIAL Variable inside the radical sign √ 3x 4x + √ 7y 5a – 3b + √ c

17. NOT A POLYNOMIAL Negative exponents. 2x + y -2 3x 4 y -1 z 3 m -3 + 8

18. NOT A POLYNOMIAL Variable in the denominator __ 2x + y__ z __1__ 2x

19. NOT A POLYNOMIAL.. If there is/are…. Variable/s inside the radical sign Negative exponent/s. Variable/s in the denominator

20. Monomial Binomial Trinomial CLASSIFICATION OF POLYNOMIALS:

21. MONOMIAL a polynomial with ONE TERM

22. Examples: x -2x xyz 5x 2 y 3 z 4 -4

23. BINOMIAL a polynomial with TWO TERMS

24. Examples: x + y 2x – 3y 4a + b 2 a 3 – bc 2 d -3m – n m + _ 1_ 2

25. TRINOMIAL a polynomial with THREE TERMS

26. Examples: x + y + z 2x – 3y – 4z a 3 – 4b + c 4

27. Classify the following polynomials: 1) 2x + 3 2 ) a 2 b 4 5x – 3y + 4z -8 3a – 2b -3 1) binomial 2) monomial 3) Trinomial 4) monomial 5) NOT a polynomial

28. What is a polynomial? How can we differentiate a polynomial from not a polynomial? What are the two parts of a term? What are the classifications of a polynomial? Differentiate each classification. REVIEW:

29. The DEGREE of a term that has only one variable is the EXPONENT of that variable. Examples: DEGREE of a polynomial:

30. The DEGREE of a polynomial that has only one variable is the HIGHEST EXPONENT appearing in any of the terms. Examples: DEGREE of a polynomial:

31. The DEGREE of a term that has only one variable is the EXPONENT of that variable. Examples: DEGREE of a polynomial:

32. The DEGREE of a polynomial in more than one variable is the highest sum of the exponents Examples: DEGREE of a polynomial:

33. Polynimial is written in desccending order, the coefficient of the first term is the leading coefficient.

34. 5x + 3x 2 – 7 Polynomial or not a Polynomial: Polynomial Classification: Trinomial Descending order: 3x 2 + 5x - 7 Degree: Leading Coefficient: 2 3

35. -5x 3 + 12/x 2 + 4x + 9 Polynomial or not a Polynomial: Classification: Descending order: Degree: 2 Leading Coefficient:

36. 8x 5 y 3 – 5x 4 y 6 + 6x 3 y 4 Polynomial or not a Polynomial: Classification: Descending order: Degree: Leading Coefficient: