Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) (ii) (iii)
(iv) (v)
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. 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 termis - 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.
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Write the coefficients of in each of the following:
(i) (ii)
(iii) (iv)
Answer :
(i)
In the above expression, the coefficient of is 1.
(ii)
In the above expression, the coefficient of is - 1.
(iii)
In the above expression, the coefficient of is.
(iv)
In the above expression, the coefficient of is 0.
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Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Answer :
Write the degree of each of the following polynomials:
(i) (ii)
(iii) (iv) 3
Answer :
Classify the following as linear, quadratic and cubic polynomial:
(i) (ii) (iii) (iv) (v)
(vi) (vii)
Answer :
Find the value of the polynomial at
(i) x = 0 (ii) x = - 1 (iii) x = 2
Answer :
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 :
Verify whether the following are zeroes of the polynomial, indicated against them.
(i) (ii)
(iii) p(x) = x^{2} - 1, x = 1, - 1 (iv) p(x) = (x + 1) (x - 2), x = - 1, 2
(v) p(x) = x^{2} , x = 0 (vi) p(x) = lx + m
(vii) (viii)
Answer :
Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5 (ii) p(x) = x - 5 (iii) p(x) = 2x + 5
(iv) p(x) = 3x - 2 (v) p(x) = 3x (vi) p(x) = ax, a ≠ 0
(vii) p(x) = cx + d, c ≠ 0, c, are real numbers.
Answer :
Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by
(i) x + 1 (ii) (iii) x
(iv) x + π (v) 5 + 2x
Answer :
Find the remainder when x^{3} - ax^{2} + 6x - a is divided by x - a.
Answer :
Check whether 7 + 3x is a factor of 3x^{3} + 7x.
Answer :
Determine which of the following polynomials has (x + 1) a factor:
(i) x^{3} + x^{2} + x + 1 (ii) x^{4} + x^{3} + x^{2} + x + 1
(iii) x^{4} + 3x^{3} + 3x^{2} + x + 1 (iv)
Answer :
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x) = 2x^{3} + x^{2} - 2x - 1, g(x) = x + 1
(ii) p(x) = x^{3} + 3x^{2} + 3x + 1, g(x) = x + 2
(iii) p(x) = x^{3} - 4 x^{2} + x + 6, g(x) = x - 3
Answer :
Use suitable identities to find the following products:
(i) (ii)
(iii) (iv)
(v)
Answer :
Evaluate the following products without multiplying directly:
(i) 103 x 107 (ii) 95 x 96 (iii) 104 x 96
Answer :
Factorise the following using appropriate identities:
(i) 9x^{2} + 6xy + y^{2}
(ii)
(iii)
Answer :
Expand each of the following, using suitable identities:
(i) (ii)
(iii) (iv)
(v) (vi)
Answer :
Factorise:
(i)
(ii)
Answer :
Write the following cubes in expanded form:
(i) (ii)
(iii) (iv)
Answer :
Evaluate the following using suitable identities:
(i) (99)^{3} (ii) (102)^{3} (iii) (998)^{3}
Answer :
Factorise each of the following:
(i) (ii)
(iii) (iv)
(v)
Answer :
Factorise each of the following:
(i)
(ii)
[Hint: See question 9.]
Answer :
If x + y + z = 0, show that .
Answer :
Without actually calculating the cubes, find the value of each of the following:
(i)
(ii)
Answer :
Give possible expressions for the length and breadth of each of thefollowing rectangles, in which their areas are given:
Answer :
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
Answer :
Maths : CBSE NCERT Exercise Solutions for Class 9th for Polynomials ( Exercise 2.1, 2.2, 2.3, 2.4, 2.5 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.
Exercise 2.1 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Exercise 2.2 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Exercise 2.3 |
Question 1 |
Question 2 |
Question 3 |
Exercise 2.4 |
Question 1 |
Question 2 |
Exercise 2.5 |
Question 1 |
Question 2 |
Question 3 |
Question 4 |
Question 5 |
Question 6 |
Question 7 |
Question 8 |
Question 9 |
Question 10 |
Question 11 |
Question 12 |
Question 13 |
Question 14 |
Question 15 |
Question 16 |