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A Review On Polynomials

A review on polynomials, monomials, binomials, trinomials and etc. This is also a review on identifying the degree of a polynomial.

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A Review On Polynomials

  1. 1. A REVIEW ON POLYNOMIALS Prepared by: Ruby Rose Ann B. Panganod,LPT
  2. 2. WHAT IS A POLYNOMIAL? - A polynomial is an algebraic expression that represents a sum of one or more terms containing whole number exponents on the variables.
  3. 3. EXAMPLES: • 7𝑥𝑦2 𝑧 • 9𝑥2 − 4𝑥 + 5 •10𝑥 + 9𝑦 − 3𝑧 • 3𝑦2 + 2𝑥2
  4. 4. Are these polynomials? •11𝑥2 − 46𝑥 − 5 • 6𝑥−1 + 8𝑦 − 5 • 1 2𝑥 + 5𝑥2 •13𝑥3 + 18 POLYNOMIAL NOT A POLYNOMIAL NOT A POLYNOMIAL POLYNOMIAL
  5. 5. Based on the number of terms, polynomials can be identified as monomial, binomial and trinomial.
  6. 6. A polynomial with one term is called a MONOMIAL. A polynomial with three terms is called a TRINOMIAL. A polynomial with two terms is called a BINOMIAL.
  7. 7. A polynomial with more than three terms have no special name.
  8. 8. EXAMPLES: MONOMIAL BINOMIAL TRINOMIAL 9𝑥2 𝑦 9𝑥2 𝑦 − 5x 9𝑥2 𝑦 − 5x + 1 5𝑏3 5𝑏3 +14𝑏2 5𝑏3 +14𝑏2 − 21𝑏 −16𝑥 −16𝑥 + 28 −16𝑥 + 18𝑦 − 28 45 5𝑏3 + 1 5𝑏3 + 5𝑎3 − 8
  9. 9. Polynomials can also be classified using their degree.
  10. 10. The degree of a monomial is the total number of times its variables occur as factors. −5𝑎𝑏2 𝑐3 EXAMPLE: The degree is 1+2+3 = 6
  11. 11. The degree of a polynomial is the greatest of the degrees of its terms. 𝑎2 𝑏 + 𝑎2 𝑏2 − 𝑎𝑏 EXAMPLE: The degree of 𝑎2 𝑏 is 3. The degree of 𝑎2 𝑏2 is 4. The degree of 𝑎𝑏 is 2. Therefore, the degree of 𝑎2 𝑏 + 𝑎2 𝑏2 − 𝑎𝑏 is 4.
  12. 12. Like terms are terms that contains the same VARIABLES and EXPONENTS. If the terms differ by at least one variable, they are called Unlike terms.
  13. 13. EXAMPLES: LIKE TERMS UNLIKE TERMS 4𝑥 𝑎𝑛𝑑 7𝑥 4𝑥 𝑎𝑛𝑑 3𝑦 5𝑏3 and 2𝑏3 −9𝑥3 and 14𝑥2 −16𝑦 𝑎𝑛𝑑 4𝑦 −16𝑥 𝑎𝑛𝑑 − 1 4𝑎2 𝑏 𝑎𝑛𝑑 5𝑎2 𝑏 5𝑎2 𝑏 𝑎𝑛𝑑 4𝑎𝑏2
  14. 14. QUIZ
  15. 15. A. Give 3 examples of the ff: 1. Monomial 2. Binomial 3. Trinomial
  16. 16. B. Tell whether each expression is a polynomial or not. 1. 1 𝑥 2. 11 + 2𝑦 3. −25𝑥3 𝑦2 𝑧 4. 25𝑥−3 𝑦2 𝑧 5. 1 𝑥−2
  17. 17. C. Give the degree of each polynomial. 1. −5𝑥 − 10𝑥2 2. 15𝑥 3. 5𝑥8 𝑦2 𝑧 4. 25𝑥3 𝑦2 𝑧 + 25𝑥3 𝑦𝑧2 − 𝑦10 5. 2𝑚𝑛3 − 4𝑚5 𝑛
  18. 18. D. Simplify by combining like terms. 1. 4𝑎 + 5𝑏 − 6𝑎 + 7𝑏 2. 5𝑥 + 9 − 6𝑥 + 7 + 4𝑦 3. 5𝑥3 + 2𝑦2 + 4𝑧 − 5𝑥3 − 4𝑦2 − 6𝑧 4. 6𝑦2 − 2𝑦2 + 8𝑦2 − 10𝑦2 5. 4𝑥 − 8𝑦 + (5𝑥 + 2𝑦)

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