2. Polynomials
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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What we have learnt
- A polynomial in one variable is an algebraic expression of the form p(x) = anxn + an–1xn–1 + ... + a2x2 + a1x + a0.
- Polynomials are classified into monomials, binomials, and trinomials based on the number of terms.
- Each polynomial has a degree which indicates the highest power of the variable in the polynomial.
Key Concepts
- -- Polynomial
- An algebraic expression consisting of variables raised to non-negative integer powers, combined with coefficients.
- -- Degree of a Polynomial
- The highest exponent of the variable in the polynomial.
- -- Zero of a Polynomial
- A value for which the polynomial evaluates to zero.
- -- Factor Theorem
- States that if p(a) = 0, then (x - a) is a factor of the polynomial p(x).
- -- Algebraic Identities
- Equations that hold true for all values of the variables in them, such as (x + y)² = x² + 2xy + y².
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