Chapter 2 Ex 2.1

                                                  Maths NCERT Book Solutions

                                                                  Chapter 2

                                                                   Ex.2.1

Q: 1

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer

Answer

(i)               Yes, this expression is a polynomial in one variable x. (ii)                Yes, this expression is a polynomial in one variable y. (iii)                 No, here the exponent of variable t in term  which is not a whole number.            So this expression is not a polynomial. (iv)                No, here the exponent of variable t in term  is -1, which is not a whole number. So this expression is not a polynomial. (v)                No, this expression is a polynomial in 3 variables x, y and t. Concept Insight: In such problems to check whether the given algebraic expressions is a polynomial or not, check the exponents of variable to be a whole number. The second step is to look for the number of variables the expression has. Any alphabet used in the expression is the variable unless specified as constant.

Q: 2 Write the coefficient of x2 in each of the following:     Answer (i)               In the above expression coefficient of x2 is 1   (ii)                In the above expression coefficient of x2 is - 1.   (iii)                   In the above expression coefficient of     (iv)                      In the above expression coefficient of x2  is 0.   Concept Insight: The constant/ variable multiplied with the variable is the coefficient of the variable. Also consider the sign (+ve or the -ve) of the term while writing the coefficient.  Q: 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 variable in the polynomial. Binomial has two terms in it. So binomial of degree 35 can be written as x2 + 7 .   Monomial has only one term in it. So monomial of degree 100 can be written as 7x100.   Concept Insight: Mono, bi and tri means one, two and three respectively. So, monomial is a polynomial having one term similarly for binomials and trinomials. Degree is the highest exponent of variable.  The answer is not unique in such problems . Remember that the terms are always separated by +ve or -ve sign and not with  .   Q: 4 Write the degree of each of the following polynomials:     Answer  Degree of a polynomial is the highest power of variable in the polynomial.             This is a polynomial in variable x and highest power of variable x is 3. So, degree of           this polynomial is 3              This is a polynomial in variable y and the highest power of variable y is 2. So degree            of this polynomial is 2.            This is a polynomial in variable t and the highest power of variable t is 1. So degree            of this polynomial is 1. (iv)      3            This is a constant polynomial. Degree of a constant polynomial is always 0.   Concept Insight: Degree is the highest  exponent of the variable. While finding the degree of a polynomial express the polynomial in standard form  Combine the like terms and Remember the result that xo = 1. Q: 5 Classify the following as linear, quadratic and cubic polynomial:   Answer (i)       2 + x2 + x  is a quadratic polynomial as its degree is 2. (ii)      x - x3 is a cubic polynomial as  its degree is 3. (iii)     y + y2 + 4  is a quadratic polynomial as its degree is 2. (iv)     1 + x is a linear polynomial as its degree is 1. (v)      3t is a linear polynomial as its degree is 1. (vi)     r2 is a quadratic polynomial as its degree is 2. (vii)     7x3 is a cubic polynomial as its degree is 3.     Concept Insight: Linear polynomial, quadratic polynomial and cubic polynomial has its degrees as 1, 2, and 3 respectively.