CBSE Class 10 Maths Notes Chapter 2 Polynomials

  • “Polynomial” comes from the word ‘Poly’ (Meaning Many) and ‘nomial’ (in this case meaning Term)-so it means many terms.
  • A polynomial is made up of terms that are only added, subtracted or multiplied.
  • A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0.
  • Degree – The highest exponent of the variable in the polynomial is called the degree of polynomial. Example: 3x3 + 4, here degree = 3.
  • Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomial respectively.
  • A polynomial can have terms which have Constants like 3, -20, etc., Variables like x and y and Exponents like 2 in y².
  • These can be combined using addition, subtraction and multiplication but NOT DIVISION.
  • The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x-axis.

Zeroes (α, β, γ) follow the rules of algebraic identities, i.e.,
(α + β)² = α² + β² + 2αβ
∴(α² + β²) = (α + β)² – 2αβ

DIVISION ALGORITHM:
If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then
p(x) = g(x) × q(x) + r(x)
Dividend = Divisor x Quotient + Remainder

Remember this!

  • If r (x) = 0, then g (x) is a factor of p (x).
  • If r (x) ≠ 0, then we can subtract r (x) from p (x) and then the new polynomial formed is a factor of g(x) and q(x).

2.1    INTRODUCTION :  
    In earlier classes, we have learnt about polynomials in one variable, their degrees, factors, multiples and zeros (or roots). In this chapter, we will study about the geometrical representation of linear quadratic  and cubic polynomials and geometrical meaning of their zeros. We will also study about the relationship between the zeros and coefficients of a polynomial. LCM and HCF of two or more polynomials, rational expressions, basic operation on polynomials and concept of square root of polynomials.