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Polynomials represent a significant class of algebraic expressions formed by combining variables, constants, and non-negative integer exponents. The chapter elaborates on various types of polynomials, their classifications based on degrees, the concepts of zeros and factors, and the application of algebraic identities in factorization. It emphasizes the importance of the Remainder and Factor Theorems in understanding polynomials in one variable as well as in multiple variables.
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Term: Polynomial
Definition: An algebraic expression consisting of variables raised to non-negative integer powers, combined with coefficients.
Term: Degree of a Polynomial
Definition: The highest exponent of the variable in the polynomial.
Term: Zero of a Polynomial
Definition: A value for which the polynomial evaluates to zero.
Term: Factor Theorem
Definition: States that if p(a) = 0, then (x - a) is a factor of the polynomial p(x).
Term: Algebraic Identities
Definition: Equations that hold true for all values of the variables in them, such as (x + y)Β² = xΒ² + 2xy + yΒ².