Page 116 - Start Up Mathematics_8 (Non CCE)

Quadratic polynomial
A polynomial of degree 2 is called a quadratic polynomial.

2
2
For example, 2x + 3x + 5, 7x – 4x + 8, Remember
3 x + x - 4 are quadratic polynomials.
2
2 3 degree 1 → linear polynomial
Polynomial of degree 2 → quadratic polynomial
Cubic polynomial degree 3 → cubic polynomial
A polynomial of degree 3 is called a cubic degree 4 → biquadratic polynomial
polynomial.
3
2
2
2
3
3
For example, 5a + 7a – 3a + 6, x – x + 5x – 7, 4p + 2p + 3 p - 1 are cubic polynomials.
2 2
Biquadratic polynomial
A polynomial of degree 4 is called a biquadratic polynomial.
4
3
2
3
2
For example, 3x – x + x – 4x + 6, 3 x + 1 x + x are biquadratic polynomials.
4
2 3
Every polynomial is an algebraic expression but not vice versa. So all the four operations i.e., addition,
subtraction, multiplication and division are done as in algebraic expressions.
EXERCISE 6.1
1. Write the degree of each of the following polynomials:

5
8
3
9
4
5
3
(a) 4x + 5x – 7 (b) 3 y - 1 y + y (c) 9 (d) 52x – 16x + 7x + 4 (e) –1
2 4
2. Which of the following expressions are not polynomials?
3
4
3
2
3
(a) x + 3x –2 (b) 2x + 3x - 4x (c) 2x 32/ + 4x + 8x + 7 (d) x – 3x + 9
2
3. Write the following polynomials in the standard form. Also write the degree.
2
3
2
2
(a) x + 4 + 3x – 7x (b) (x –1)(x + 4)
Ê 5 ˆ Ê ˆ 6 3 3
(c) Á Ë x + 6 ˜ Á x + ˜ ¯ 5 (d) (x – 7)(x – 8)
¯ Ë
Division of a Monomial by a Monomial
Division of a monomial A by a monomial B means finding a monomial C such that A = BC. Thus, A =C
B
where A is the dividend, B is the divisor and C is the quotient.
l The coefficient of the quotient of two monomials is equal to the quotient of their coefficients.
l The variable in the quotient of two monomials is equal to the quotient of the variables in the given monomials.
5 3 4
2
2 2
3
3 2
4 3 2
Example 1: Divide: (a) 15x y by 5x y (b) –24x y z by 4x y (c) –52a b c by –2a bc 2
3
2
3 2
Solution: (a) 15x y ÷ 5x y = 15xy 2 = 15 ¥ x 3 ¥ y 2
2
5xy 5 x 2 y
n
m
= 3 × x 3 – 2 × y 2 – 1 = 3xy ( x ÷ x = x m – n )
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