Classifying Polynomials

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Classifying Polynomials

  1. 1. CLASSIFYING ALGEBRAIC EXPRESSIONS<br />
  2. 2. REVIEW/DRILL:Translate the given Algebraic Expression to English Phrase.<br />6m – 5<br />x + y + z<br />3(ab)<br />
  3. 3. REVIEW/DRILL:Translate the given Algebraic Expression to English Phrase.<br />5m<br />2n<br />3x + y <br />
  4. 4. REVIEW/DRILL:Translate the given Algebraic Expression to English Phrase.<br />25 + ab<br />3 (m + n)<br />_1_x<br /> 4<br />
  5. 5. Define:<br />“mono”“bi”“tri”“poly”<br />
  6. 6. Define the word “mono”<br />CLUE:<br />
  7. 7. Define the word “bi”<br />CLUE:<br />
  8. 8. Define the word “tri”<br />CLUE:<br />
  9. 9. Define the word “poly”<br />CLUE:<br />
  10. 10. POLYNOMIAL<br />an algebraic expression that represents a sum of ONE or MORE TERMS containing whole number exponents on the variables<br />
  11. 11. Remember the parts of a term?<br />
  12. 12. NUMERICAL COEFFICIENT<br /><ul><li>The number in an algebraic term.</li></li></ul><li>LITERAL COEFFICIENT<br /><ul><li>A letter used to represent a number</li></li></ul><li>EXAMPLES:<br />4 x<br />Numerical coefficient Literal coefficient<br /><ul><li>45 abc </li></ul>Numerical coefficient Literal coefficient<br />
  13. 13. Examples:<br />3xy<br />2x + y<br />x2 – 2x + 6<br />2x3 - x2 + 4x - 10<br />
  14. 14. NOT A POLYNOMIAL<br />Variable inside the radical sign<br />√ 3x<br />4x + √ 7y<br />5a – 3b + √ c<br />
  15. 15. NOT A POLYNOMIAL<br />Negative exponents.<br />2x + y -2<br />3x4 y-1 z3<br />m-3 + 8<br />
  16. 16. NOT A POLYNOMIAL<br />Variable in the denominator<br />__2x + y__<br />z<br />__1__<br />2x<br />
  17. 17. NOT A POLYNOMIAL..<br />If there is/are….<br />Variable/s inside the radical sign<br />Negative exponent/s.<br />Variable/s in the denominator<br />
  18. 18. CLASSIFICATION OF POLYNOMIALS:<br />Monomial<br />Binomial<br />Trinomial<br />
  19. 19. MONOMIAL<br />a polynomial with ONE TERM<br />
  20. 20. Examples:<br />x -2x<br /> xyz 5x2 y3 z <br /> 4 -4 <br />
  21. 21. BINOMIAL<br />a polynomial with <br />TWO TERMS<br />
  22. 22. Examples:<br />x + y 2x – 3y<br /> 4a + b2 a3 – bc2d<br />-3m – n m + _1_<br /> 2<br />
  23. 23. TRINOMIAL<br />a polynomial with <br />THREE<br />TERMS<br />
  24. 24. Examples:<br />x + y + z<br />2x – 3y – 4z<br />a3 – 4b + c4<br />
  25. 25. Classify the following polynomials:<br />1) binomial<br />2) monomial<br />3) Trinomial<br />4) monomial<br />5) NOT a polynomial<br />1) 2x + 3<br />2) a2 b4<br />5x – 3y + 4z<br /> -8<br /> 3a – 2b -3<br />
  26. 26. REVIEW:<br />What is a polynomial? <br />How can we differentiate a polynomial from not a polynomial?<br />What are the two parts of a term?<br />What are the classifications of a polynomial? <br />Differentiate each classification.<br />
  27. 27. DEGREE of a polynomial:<br />The DEGREE of a term that has only one variable is the EXPONENT of that variable.<br />Examples:<br />
  28. 28. DEGREE of a polynomial:<br />The DEGREEof a polynomial that has only one variable is the HIGHEST EXPONENTappearing in any of the terms.<br />Examples:<br />
  29. 29. DEGREE of a polynomial:<br />The DEGREE of a term that has only one variable is the EXPONENT of that variable.<br />Examples:<br />
  30. 30. DEGREE of a polynomial:<br />The DEGREE of a polynomial in more than one variable is the highest sum of the exponents<br />Examples:<br />
  31. 31. Polynimial is written in desccendingorder, the coefficient of the first term is the leading coefficient.<br />
  32. 32. 5x + 3x2 – 7<br />Polynomial or not a Polynomial:<br /> Polynomial<br />Classification:<br /> Trinomial<br />Descending order:<br /> 3x2 + 5x - 7<br />Degree:<br />Leading Coefficient: <br />2<br />3<br />
  33. 33. -5x3 + 12/x2 + 4x + 9<br />Polynomial or not a Polynomial:<br />Classification:<br />Descending order:<br />Degree: 2<br />Leading Coefficient: <br />
  34. 34. 8x5 y3 – 5x4 y6 + 6x3 y4<br />Polynomial or not a Polynomial:<br />Classification:<br />Descending order:<br />Degree: <br />Leading Coefficient: <br />

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