A Review On Polynomials
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The document provides a review of polynomials, defining them as algebraic expressions consisting of terms with whole number exponents. It categorizes polynomials based on their number of terms (monomial, binomial, trinomial) and discusses their degrees and identification of like and unlike terms. Additionally, it includes a quiz section with tasks related to examples, classification, degree determination, and simplification of polynomials.
A Review On Polynomials
- 1. A REVIEW ON POLYNOMIALS Prepared by: Ruby Rose Ann B. Panganod,LPT
- 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. EXAMPLES: • 7𝑥𝑦2 𝑧 • 9𝑥2 − 4𝑥 + 5 •10𝑥 + 9𝑦 − 3𝑧 • 3𝑦2 + 2𝑥2
- 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. Based on the number of terms, polynomials can be identified as monomial, binomial and trinomial.
- 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. A polynomial with more than three terms have no special name.
- 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. Polynomials can also be classified using their degree.
- 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. 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. 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. 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. QUIZ
- 15. A. Give 3 examples of the ff: 1. Monomial 2. Binomial 3. Trinomial
- 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. 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. 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)