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1. Real Numbers
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
2. Polynomials
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise 2.4
3. Pair of Linear Equations in Two Variables
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Exercise 3.5
Exercise 3.6
Exercise 3.7
4. Quadratic Equations
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
5. Arithmetic Progressions
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
6. Triangles
Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise 6.4
Exercise 6.5
Exercise 6.6
Ncert Solutions for Class 10 Maths
Exercise 2.3 (Division Algorithm for Polynomials)
1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
(i) \(p(x) = x^3 – 3x^2 + 5x – 3\), \(g(x) = x^2 – 2\)
(ii) \(p(x) = x^4 – 3x^2 + 4x + 5\), \(g(x) = x^2 + 1 – x\)
(iii) \(p(x) = x^4 – 5x + 6\), \(g(x) = 2 – x^2\)
2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :
(i) \(t^2 – 3\), \(2t^4 + 3t^3 – 2t^2 – 9t – 12\)
(ii) \(x^2 + 3x + 1\), \(3x^4 + 5x^3 – 7x^2 + 2x + 2\)
(iii) \(x^3 – 3x + 1\), \(x^5 – 4x^3 + x^2 + 3x + 1\)
3. Obtain all other zeroes of \(3x^4 + 6x^3 – 2x^2 – 10x – 5\), if two of its zeroes are \(\sqrt{5\over 3}\) and \(-\sqrt{5\over 3}\).
4. On dividing \(x^3 – 3x^2 + x + 2\) by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).
5. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0
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Division Algorithm for Polynomials (Video) [Full Exercise 2.3]
Ncert Solution for Class 10 (Mathematics)
Important Class 10 Links
1. Real Numbers
2. Polynomials
3. Pair of Linear Equations in Two Variables
4. Quadratic Equations
5. Arithmetic Progressions
6. Triangles