Page 135 - ICSE Math 6

Polynomial

An algebraic expression which consists of finite number of non-zero terms with powers of variables
in whole numbers is called a polynomial.

Degree of a polynomial
Maths Info
The degree of a polynomial is the highest power of the literal(s) in
its terms. For example, Every polynomial is an algebraic
(a) 7 is a constant polynomial with degree 0. expression but an expression need
not to be a polynomial. For example,
2
3

(b) x + 3x – 9x is a polynomial in x with degree 3. x and are expressions but not
1
m
4
5
2
(c) a + 2a – a is a polynomial in a with degree 5. polynomials.
3
2
3
Example 7: Write all the terms of the algebraic expression 2a – a + 5ab + 10. Also, write its
constant terms.
3
2
Solution: The four terms of the given algebraic expression are 2a , –a , 5ab and 10.
Its constant term is 10.
Example 8: Classify the following algebraic expressions as monomial, binomial or trinomial.
(a) 12y + 6x – 7 (b) 100x (c) –7xy + x 2
Solution: (a) The algebraic expression 12y + 6x – 7 has 3 terms namely, 12y, 6x and –7. Therefore,
it is a trinomial.

(b) The algebraic expression 100x has only 1 term which is 100x. Therefore, it is a
monomial.
2
2
(c) The algebraic expression –7xy + x has only 2 terms which are –7xy and x .
Therefore, it is a binomial.
Example 9: Which of the following algebraic expressions are polynomials? Also, find the degree
of the polynomials.

3
(a) 1 + 2a + 21a (b) –4x + x – 7 (c) 1 y + 1
2
3 x 11 11
Solution: (a) Yes, it is a polynomial in a.
3
Degree of polynomial = 3 (Q exponent of a = 3)
− 7
(b) No, it is not a polynomial as the degree of x in the term is –1.
(c) Yes, it is a polynomial in y. x

Degree of polynomial = 1 (Q exponent of y = 1)

EXERCISE 11.2

1. Identify the numerical factor of each term of the expression:
2
2
2
2
(a) 3x + 2y – x (b) x y + 3 xz + 5z
3 11
2. Group the like terms together.
3 − 2 2
(a) 2a, 3b, a, –6b, a (b) 4xy, –4y, –14yx, y
5 3 11

119