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Polynomials - Class IX CBSE Mathematics | NCERT Solutions for Math Textbook Exercise 2.1

POLYNOMIALS
   Class IX NCERT (CBSE) Mathematics
   NCERT Textbook Exercise 2.1 Solved
(page 32)
Q1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
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Answer:
(i) It is a polynomial in one variable x.
(ii) This expression is a polynomial in one variable y.
(iii) Since exponent of variable t in term
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which is not a whole number, so this expression is not a polynomial.

(iv) Since the exponent of variable y in term
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Hence, this expression is not a polynomial.

(v) No it is not a polynomial in one variable. This expression is a polynomial in 3 variables x, y, and t
Q2: Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x (ii) 2 – x2 + x3
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Answer:
(i) The coefficient of x2 is 1.
(ii) In this expression, the coefficient of x2 is −1.
(iii) Here the coefficient of x2 is π/2.
(iv) In the above expression, the coefficient of x2 is 0.
Q3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Answer:  
By definition, the 'Degree of a Polynomial' is the highest power of the variable in the polynomial. 
A binomial has two terms in it. An example of binomial of degree 35 is x35 + x34.
A Monomial has only one term in it. An example of monomial of degree 100 is x100.
Q4: Write the degree of each of the following polynomials:
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Answer:
(i) It is a polynomial in variable x and the highest power of variable x is 3. Therefore, the degree of this polynomial is 3.
(ii) The given polynomial has variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.
(iii) This expression is a polynomial of variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.
(iv) Since it is a constant polynomial and the degree of a constant polynomial is always 0.
Q5: Classify the following as linear, quadratic and cubic polynomial:
(i) x2 + x (ii) x – x3 (iii) y + y2 + 4 (iv) 1 + x (v) 3t
(vi) r2 (vii) 7x3
Answer: Linear, quadratic, and cubic polynomials have degrees as 1, 2, and 3 respectively.
(i) This is a quadratic polynomial as its degree is 2.
(ii) This is a cubic polynomial as its degree is 3.
(iii) This is a quadratic polynomial and its degree is 2.
(iv) 1 + x is a linear polynomial. Its degree is 1.
(v) 3t is a linear polynomial. Its degree is 1.
(vi) r2 is a quadratic polynomial as its degree is 2.
(vii) 7x3 is a cubic polynomial and its degree is 3.

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