POLYNOMIALS

POLYNOMIALS

1. COMPONENTS:

   • Variables
   • Constant
   • Co-effcient
   • Term
   • Degree
     • Degree 1: Linear Polynomial
     • Degree 2: Quadratic polynomial
     • Degree 3: Cubic Polynomial
     • Degree 4: Biquadratic Polynomial

2. TYPES OF POLYNOMIALS

   • Monomial: A polynomial with one term
   • Binomial: A polynomial with two terms
   • Trinomial: A polynomial with three terms
   • Polynomial: A polynomial with 4 or more terms

3. ZERO OF A POLYNOMIAL

   • The value of p(x) at x=k
   • Generally k is called the zero of a polynomial

4. GRAPHICAL REPRESENTATION

   • Linear polynomials: Zeroes intersect at exactly one point on either axes
   • Quadratic polynomials: Zeroes intersects at two points (on x-axis) and forms a parabola

5. RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS

   • SUM OF ZEROES:
     • alpha + beta
     • -b / a
   • PRODUCT OF ZEROES:
     • alpha x beta
     • c / a
   • IDENTIFYING POLYNOMIAL WHEN ZEROES ARE GIVEN
     • x^2 - (alpha + beta) x + alpha x beta

6. DIVISION ALGORITHM

   • If p(x) and g(x) are any two polynomials with g(x) is not 0, we can find q(x) and r(x) by
     • p(x)=g(x) x q(x) + r(x)