Polynomials — Chapter Summary

A polynomial in one variable

A polynomial in one variable is an algebraic expression of the form: p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀, where aₙ, aₙ₋₁, ..., a₁, a₀ are real num

Polynomials are classified by their degree

Polynomials are classified by their degree: (1) Linear polynomial (degree 1): p(x) = ax + b, where a ≠ 0. Examples: 2x - 3, √3x + 5. (2) Quadratic pol

If p(x) is a polynomial

If p(x) is a polynomial and k is any real number, the value obtained by replacing x with k in p(x) is called p(k), the value of p(x) at x = k. Example

A real number k is called

A real number k is called a zero of a polynomial p(x) if p(k) = 0. In other words, when we substitute k for x and the result equals zero, then k is a

For a linear polynomial p(x) =

For a linear polynomial p(x) = ax + b (a ≠ 0), the graph of y = ax + b is a straight line. The zero of the polynomial is the x-coordinate of the point