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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)
, 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 .
(iv)
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
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,NCRTSOLUTIONS.BLOGSPOT.COM
.
Monomial has only one term in it. Therefore, monomial of degree 100 can be written as
x100.
Question 4:
Write the degree of each of the following polynomials:
(ii) (i)
(iv) 3 (iii)
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)
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.
NCRTSOLUTIONS.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)
, 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 .
(iv)
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
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,NCRTSOLUTIONS.BLOGSPOT.COM
.
Monomial has only one term in it. Therefore, monomial of degree 100 can be written as
x100.
Question 4:
Write the degree of each of the following polynomials:
(ii) (i)
(iv) 3 (iii)
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)
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.
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