Polynomials — Chapter Summary

A polynomial p(x) is an algebraic

A polynomial p(x) is an algebraic expression of the form anxn + an-1xn-1 + ... + a1x + a0, where coefficients are constants and an ≠ 0. The exponents

By degree

By degree: Linear (degree 1), Quadratic (degree 2), Cubic (degree 3). By terms: Monomial (1 term), Binomial (2 terms), Trinomial (3 terms). Examples:

A zero of polynomial p(x)

A zero of polynomial p(x) is a value 'a' such that p(a) = 0. For linear polynomial ax + b, the zero is x = -b/a. Every linear polynomial has exactly o

If p(a) = 0

If p(a) = 0, then (x - a) is a factor of p(x). Conversely, if (x - a) is a factor of p(x), then p(a) = 0. This connects zeroes with factorization.

Breaking down polynomials into products

Breaking down polynomials into products of simpler factors. For ax² + bx + c, split middle term b into two parts whose product equals ac. Example: 6x²