Page 138 - ICSE Math 7

5
3
(a) –8a + 5a – is a polynomial in a with degree 3. Maths Info
3
(b) 10 is a constant polynomial with degree 0. A polynomial consisting of only
a constant term is known as a
Point to remember constant polynomial.
1 1 1
A polynomial in x can have a constant term, but it cannot have terms containing , , , etc.
x x 2 x 3
Polynomial in two or more variables
An algebraic expression in which the exponents of two or more variables are non-negative integers
is called a polynomial in two or more variables. To find the degree of a polynomial in two or more
variables, find the sum of the powers of the variables in each term. The highest sum is the degree of
the polynomial. Example:
2
2
(a) 3x y + 5y – 7xy + 8x is a polynomial in x and y. Try This
2
Sum of the powers of x and y in 3x y = 2 + 1 = 3 Identify the degree of the
2
Sum of the powers of x and y in 5y = 0 + 2 = 2 following polynomials:
2
Sum of the powers of x and y in –7xy = 1 + 1 = 2 (a) a + ab + b 2
2
2
(b) 4x y + 2x – 2y + 18
Sum of the powers of x and y in 8x = 1 + 0 = 1 (c) 3p q + q p
3
2
3
3
As the highest sum is 3, therefore the degree of the given polynomial (d) 2ab c + 3a b
is 3.
1 2 2
2
2
3
(b) 7 a + b – a b + 2a is a polynomial in a and b with degree 4.
15 5
Example 1: (a) Form expressions using m and 6. Use not more than one number operation. Every
expression must have m in it.
(b) Form expression using x, 2 and 5. Every expression must have x in it. Use only two
number operations. These should be different.
,
Solution: (a) m + 6, m – 6, 6 – m, 6m, m 6 (m ≠ 0)
6 m
,
(b) 2x + 5, 2x –5, 5x + 2, 5x – 2, 2x 5x
5 2
2 2
3
3 2
Example 2: For the algebraic expression 8 – 7xy + 5x y – 13xy + 6x y , find:
3
3
(a) the number of terms. (b) the coefficient of (–xy ) in –13xy .
2
3 2
2 2
(c) the coefficient of x in 6x y . (d) the literal coefficient in 5x y .
(e) the numerical coefficient in –7xy. (f) the degree of the polynomial.
3
2 2
3 2
Solution: (a) Different terms of the polynomial are 8, –7xy, 5x y , –13xy and 6x y .
\ Number of terms = 5
3
3
(b) Coefficient of –xy in –13xy = 13
2
2 2
(c) Coefficient of x in 6x y = 6y 2
3 2
3 2
(d) Literal coefficient in 5x y = x y
(e) Numerical coefficient in –7xy = –7
(f) Degree of the polynomial = 5
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