Page 1 Cbse-spot.blogspot.com Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial. (iv) Page 2 Cbse-spot.blogspot.com Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial. (iv) Cbse-spot.blogspot.com No. It can be observed that the exponent of variable y in term is -1, which is not a whole number. Therefore, this expression is not a polynomial. (v) No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable. In the above expression, the coefficient of is -1. (iii) In the above expression, the coefficient of In the above expression, the coefficient of is 0. Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100. Answer: Degree of a polynomial is the highest power of the variable in the polynomial. Binomial has two terms in it. Therefore, binomial of degree 35 can be written as . Monomial has only one term in it. Therefore, monomial of degree 100 can be written as x 100 . Question 2: Write the coefficients of in each of the following: In the above expression, the coefficient of is 1. ( ii ) ( i) ( ii) ( iii) ( iv) Answer: ( i) . is ( iv) Page 3 Cbse-spot.blogspot.com Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial. (iv) Cbse-spot.blogspot.com No. It can be observed that the exponent of variable y in term is -1, which is not a whole number. Therefore, this expression is not a polynomial. (v) No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable. In the above expression, the coefficient of is -1. (iii) In the above expression, the coefficient of In the above expression, the coefficient of is 0. Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100. Answer: Degree of a polynomial is the highest power of the variable in the polynomial. Binomial has two terms in it. Therefore, binomial of degree 35 can be written as . Monomial has only one term in it. Therefore, monomial of degree 100 can be written as x 100 . Question 2: Write the coefficients of in each of the following: In the above expression, the coefficient of is 1. ( ii ) ( i) ( ii) ( iii) ( iv) Answer: ( i) . is ( iv) Cbse-spot.blogspot.com Question 4: Write the degree of each of the following polynomials: Answer: Degree of a polynomial is the highest power of the variable in the polynomial. (i) This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3. (ii) This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2. (iii) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1. (iv) 3 This is a constant polynomial. Degree of a constant polynomial is always 0. Question 5: Classify the following as linear, quadratic and cubic polynomial: (i) (vi) ( i) ( iii) ( ii) ( iv) 3 ii) ( ( iii) ( iv) ( v) ( vii) Page 4 Cbse-spot.blogspot.com Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial. (iv) Cbse-spot.blogspot.com No. It can be observed that the exponent of variable y in term is -1, which is not a whole number. Therefore, this expression is not a polynomial. (v) No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable. In the above expression, the coefficient of is -1. (iii) In the above expression, the coefficient of In the above expression, the coefficient of is 0. Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100. Answer: Degree of a polynomial is the highest power of the variable in the polynomial. Binomial has two terms in it. Therefore, binomial of degree 35 can be written as . Monomial has only one term in it. Therefore, monomial of degree 100 can be written as x 100 . Question 2: Write the coefficients of in each of the following: In the above expression, the coefficient of is 1. ( ii ) ( i) ( ii) ( iii) ( iv) Answer: ( i) . is ( iv) Cbse-spot.blogspot.com Question 4: Write the degree of each of the following polynomials: Answer: Degree of a polynomial is the highest power of the variable in the polynomial. (i) This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3. (ii) This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2. (iii) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1. (iv) 3 This is a constant polynomial. Degree of a constant polynomial is always 0. Question 5: Classify the following as linear, quadratic and cubic polynomial: (i) (vi) ( i) ( iii) ( ii) ( iv) 3 ii) ( ( iii) ( iv) ( v) ( vii) Cbse-spot.blogspot.com Answer: Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively. (i) is a quadratic polynomial as its degree is 2. (ii) is a cubic polynomial as its degree is 3. (iii) is a quadratic polynomial as its degree is 2. (iv) 1 + x is a linear polynomial as its degree is 1. (v) is a linear polynomial as its degree is 1. (vi) is a quadratic polynomial as its degree is 2. (vii) is a cubic polynomial as its degree is 3. Page 5 Cbse-spot.blogspot.com Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial. (iv) Cbse-spot.blogspot.com No. It can be observed that the exponent of variable y in term is -1, which is not a whole number. Therefore, this expression is not a polynomial. (v) No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable. In the above expression, the coefficient of is -1. (iii) In the above expression, the coefficient of In the above expression, the coefficient of is 0. Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100. Answer: Degree of a polynomial is the highest power of the variable in the polynomial. Binomial has two terms in it. Therefore, binomial of degree 35 can be written as . Monomial has only one term in it. Therefore, monomial of degree 100 can be written as x 100 . Question 2: Write the coefficients of in each of the following: In the above expression, the coefficient of is 1. ( ii ) ( i) ( ii) ( iii) ( iv) Answer: ( i) . is ( iv) Cbse-spot.blogspot.com Question 4: Write the degree of each of the following polynomials: Answer: Degree of a polynomial is the highest power of the variable in the polynomial. (i) This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3. (ii) This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2. (iii) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1. (iv) 3 This is a constant polynomial. Degree of a constant polynomial is always 0. Question 5: Classify the following as linear, quadratic and cubic polynomial: (i) (vi) ( i) ( iii) ( ii) ( iv) 3 ii) ( ( iii) ( iv) ( v) ( vii) Cbse-spot.blogspot.com Answer: Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively. (i) is a quadratic polynomial as its degree is 2. (ii) is a cubic polynomial as its degree is 3. (iii) is a quadratic polynomial as its degree is 2. (iv) 1 + x is a linear polynomial as its degree is 1. (v) is a linear polynomial as its degree is 1. (vi) is a quadratic polynomial as its degree is 2. (vii) is a cubic polynomial as its degree is 3. Cbse-spot.blogspot.com Exercise 2.2 Question 1: Find the value of the polynomial at (i) x = 0 (ii) x = -1 (iii) x = 2 Find p(0), p(1) and p(2) for each of the following polynomials: (i) p(y) = y 2 - y + 1 (ii) p(t) = 2 + t + 2t 2 - t 3 (iii) p(x) = x 3 (iv) p(x) = (x - 1) (x + 1) Answer: (i) p(y) = y 2 - y + 1 p(0) = (0) 2 - (0) + 1 = 1 p(1) = (1) 2 - (1) + 1 = 1 p(2) = (2) 2 - (2) + 1 = 3 (ii) p(t) = 2 + t + 2t 2 - t 3 p(0) = 2 + 0 + 2 (0) 2 - Answer: ( i) ( ii) ( iii) Question 2:Read More

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