NCERT Book Class 10 Maths Chapter 2 Polynomials

10 MATHEMATICS

POLYNOMIALS 2
2.1 Introduction

In Class IX, you have studied polynomials in one variable and their degrees. Recall
that if p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of
the polynomial p(x). For example, 4x + 2 is a polynomial in the variable x of
degree 1, 2y2 – 3y + 4 is a polynomial in the variable y of degree 2, 5x3 – 4x2 + x – 2
3 4
is a polynomial in the variable x of degree 3 and 7u6 – u  4u 2  u  8 is a polynomial
2
1 1
in the variable u of degree 6. Expressions like , x  2, etc., are
x 1 x  2x  3
2

not polynomials.
A polynomial of degree 1 is called a linear polynomial. For example, 2x – 3,
2 2
3 x  5, y  2 , x  , 3z + 4, u  1 , etc., are all linear polynomials. Polynomials
11 3
2 3
such as 2x + 5 – x , x + 1, etc., are not linear polynomials.
A polynomial of degree 2 is called a quadratic polynomial. The name ‘quadratic’
2,
has been derived from the word ‘quadrate’, which means ‘square’. 2 x 2  3x 
5
u 2 1
y 2 – 2, 2  x 2  3 x,  2u 2  5, 5v 2  v, 4 z 2  are some examples of
3 3 7
quadratic polynomials (whose coefficients are real numbers). More generally, any
quadratic polynomial in x is of the form ax2 + bx + c, where a, b, c are real numbers
and a  0. A polynomial of degree 3 is called a cubic polynomial. Some examples of