2. POLYNOMIALS
Polynomials are algebraic expressions formed by variables and coefficients, with varying degrees and terms. This chapter elaborates on types of polynomials, their zeroes, and the factorization methods including the Remainder and Factor Theorems. The chapter also discusses algebraic identities, their applications in factorization, and provides various exercises to understand the concept better.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- A polynomial p(x) in one variable x is an algebraic expression of the form p(x) = ax^n + ax^(n-1) + ... + a.
- Polynomials can be classified into monomials, binomials, and trinomials based on the number of terms.
- The Factor Theorem states that x - a is a factor of a polynomial p(x) if p(a) = 0.
Key Concepts
- -- Polynomial
- An algebraic expression consisting of variables raised to non-negative integer powers, combined by addition, subtraction, or multiplication.
- -- Degree of a Polynomial
- The highest power of the variable in the polynomial expression.
- -- Zeroes of a Polynomial
- Values of x for which the polynomial evaluates to zero.
- -- Remainder Theorem
- States that the remainder of the division of a polynomial p(x) by (x - a) is equal to p(a).
- -- Factor Theorem
- States that (x - a) is a factor of the polynomial p(x) if and only if p(a) = 0.
Additional Learning Materials
Supplementary resources to enhance your learning experience.