0What is a Polynomial?
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A polynomial is an algebraic expression made up of one or more terms.
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Each term is a combination of numbers and variables.
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Polynomials are used in algebra, graphs, and modeling real-life situations.
2. Terms of a Polynomial
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Term: A single part of a polynomial.
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Example: In “3x + 5”, 3x and 5 are terms.
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Terms can include:
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Coefficients → the number in front of the variable (like 3 in 3x)
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Variables → letters representing unknowns (like x, y)
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Exponents → power of the variable (like x², x³)
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3. Types of Polynomials (Based on Number of Terms)
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Monomial: 1 term
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Example: 7x
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Binomial: 2 terms
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Example: x + 5
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Trinomial: 3 terms
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Example: x² + 2x + 1
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Polynomial with more than 3 terms – called polynomial
4. Degree of a Polynomial
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The degree is the highest power of the variable in the polynomial.
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Important for classifying polynomials and understanding their behavior in graphs.
5. Addition and Subtraction of Polynomials
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Polynomials can be added or subtracted by combining like terms.
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Like terms have the same variable and same exponent.
Example (conceptual):
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Combine x² terms with x² terms, constants with constants.
6. Multiplication of Polynomials
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Polynomials can be multiplied by distributing each term of one polynomial to every term of the other.
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The resulting expression is still a polynomial.
7. Factorization of Polynomials
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Factorization means breaking a polynomial into simpler expressions that multiply to give the original polynomial.
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Common methods:
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Take out common factors
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Group terms
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Use special formulas (like square of a sum, difference of squares)
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8. Zeros of a Polynomial
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A zero is a value of the variable that makes the polynomial equal to zero.
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Finding zeros is important for solving equations and graphing polynomials.
9. Key Notes for Exams
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Polynomial = sum of terms with numbers and variables.
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Monomial = 1 term, Binomial = 2 terms, Trinomial = 3 terms.
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Degree = highest exponent.
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Addition/Subtraction = combine like terms.
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Multiplication = distribute terms.
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Factorization = split into simpler multiplying expressions.
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Zeros = values making polynomial zero.
