EX 2.1 QUESTION 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
The given equation has x is the only variable. So, the polynomial in one variable.
The given equation has y is the only variable. So, the polynomial in one variable.
= 3 √t1/2 + √2.t
It is in one variable but not polynomial because it contains (t1/2) which is not a whole number.
= y + 2.y-1
It is in one variable but not polynomial because it contains (y-1) which is not a whole number.
It is a polynomial in three variables x, y and t. So, it is not a polynomial in one variable.
EX 2.1 QUESTION 2.
Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x.
The coefficient of x2 is 1.
(ii) 2 – x2 + x3.
The coefficient of x2 is -1.
(iii) + x.
The coefficient of x2 is .
(iv) √2 x – 1.
The coefficient of x2 is 0.
EX 2.1 QUESTION 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
(i) A binomial of degree 35 = 3x35 -4.
(ii) A monomial of degree 100 = 3x100.
EX 2.1 QUESTION 4.
Write the degree of each of the following polynomials.
(i) 5x3+4x2 + 7x
(ii) 4 – y2
(iii) 5t – √7
(i) The degree of 5x3 + 4x2 + 7x = 3.
(ii) The degree of 4- y2 = 2.
(iii) The degree of 5t – √7 = 5t1 – √7 = 1
(iv) The degree of 3 = 3x° = 0 [∵ x°=1]