A polynomial in x is an expression containing the sum of a finite number of terms of the
form axn
for a real number a, where a ¹ 0 and a whole number n.
Polynomials
Not polynomials
2x
4x1/2
1/3x-4
3x2+4x-1+5
x2-2x-1
4+1/x
not a polynomial? Discuss with your friends and teacher.
3.2.1 DEGREE OF A POLYNOMIAL
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, 3x + 5 is a polynomial in the variable x. It is of degree 1 and
is called a linear polynomial. 5x, 2 5 y∗ ,
1
3
P, m + 1 etc. are some more linear polynomials.
A polynomial of degree 2 is called a quadratic polynomial.
For example, x
2
+ 5x + 4 is
a quadratic polynomial in the variable x. 2x
2
+ 3x -
1
2
, p
2
-1, 3 – z – z
2
, y
2
- 3
y
+ 2 are some
examples of quadratic polynomials.
The expression 5x
3–4x
2+x–1 is a polynomial in the variable x of degree 3, and is called
a cubic polynomial.
Some more examples of cubic polynomials are 2 – x
3
, p
3
, l
3
– l
2 – l + 5.
6 can be written as 6´ x
0
. As the index of x is 0, it is a polynomial of 0 degree.
3.2.1 DEGREE OF A POLYNOMIAL
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).