# NCERT Solutions for Class 9 Maths Chapter 2

Free download NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1, 2.2, 2.3, 2.4 and 2.5 of Polynomials in English Medium and Hindi Medium to use. Class 9 Maths all chapters solutions are also given in PDF. If don’t want to download, use it online.

## NCERT Solutions for Class 9 Maths Chapter 2

If you need solutions in Hindi, Click for Hindi Medium solutions of 9 Maths Chapter 2

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### 9 Maths Chapter 2 All Exercises in Hindi

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Next Chapter: Chapter 3

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##### Class 9 Maths – Polynomials
1. Write the coefficient of y³ in 5y³ + 2y² – y + 5. [Answer: 5]
2. Find the coefficient of x² in (x² – 1) (x – 2). [Answer: -2]
3. If (x – 2) is one of the factor of 3x – 2a, then find the value of a. [Answer: 3]
4. If p(x) = x³ – 3x² + 2x – 3 find the value of p(1) + p(–1). [Answer: -12]
5. Find zeros of the polynomial z² – 8. [Answer: -2√2, 2√2]
6. Dividend = Divisor × Quotient + ____________. [Answer: Remainder]
7. Give an example of Trinomial of degree 3. [Answer: x³ – 3x + 1]
8. Give one example of each monomial, binomial and quadratic polynomial. [Answer: 3x, x + 2, 2x² + x – 2]
9. Check whether x = 3 is zero of polynomial x² – 3x + x – 3. [Answer: Yes]
10. Write the degree of the polynomial √7. [Answer: 0]
11. If one of the zero of polynomial 3x² + 5x + k is –1, then find out the value of k. [Answer: 2]
12. Express 4x² – 4x + 1 as a square of binomial. [Answer: (2x – 1)²]
13. Check whether q(x) is a multiple of r(x) or not. If q(x) = 2x³ – 11x² – 4x + 5, r(x) = 2x + 1. [Answer: No]
14. Show that (x – 5) is a factor of x³ – 3x² – 4x – 30 by Remainder theorem.
15. Under tree plantation programme students of Class VIII and IX planted (3x² – 4x – 4) trees in school.
(a) If number of students in those classes are (x – 2) then find out number of trees planted by them.
(b) What values of students are exhibited here? [Answer: (a). (3x + 2), (b). Scientific attitude, environment awareness, social values]
16. Evaluate by using suitable identify: (997)³. [Answer: 991026973]
17. Find the zeros of the polynomial p(x) = x (x – 2) (x + 3). [Answer: 0, 2, – 3]
18. Find the quotient when 3x² – 7x – 6 is divided by (x – 3). [Answer: 3x + 2]
19. Factorise 8x³ + √27 y³. [Answer: (2x + √3y)(4x² – 2√3xy + 3y²)]
20. If p(x) = x + 9, then find p(x) + p(–x). [Answer: 18]
21. Expand using suitable identity (2x –3y + z)². [Answer: 4x² + 9y² + z² – 12xy – 6yz + 4xz]
22. A principal of school wants to distribute some material of volume (x³ + 9x² + 27x + 27) cubic unit. Each topper will receive quantity of material equal to dimensions of the material. State whether (i) It is possible to find the quantity of material distributed to each topper. (ii) Which moral values are depicted? [Answer: Equal amount (x + 3) unit, Motivation without discrimination]
23. Using identity, find the value of (351)² – (350)². [Answer: 701]
24. Factorise 64a² + 96ab + 36b². [Answer: (8a + 6b)²]
25. Factorise x³ + 6x² + 11x + 6. [Answer: (x + 1)(x + 2)(x + 3)]
26. If x² + y² = 49 and x – y = 3, then find the value of x² – y². [Answer: 207]
27. Simplify (5a – 2b) (25a² + 10ab + 4b²) – (2a + 5b) (4a² – 10ab + 25b²). [Answer: 117a³ – 133b³]
28. Find the sum of remainders when x³ – 3x² + 4x – 4 is divided by (x – 1) and (x + 2). [Answer: -34]
29. Simplify (3x – 4y)³ – (3x + 4y)³. [Answer: – 128y³ – 216x²y]
30. Simplify (x + y + z)² – (x – y – z)². [Answer: 4xy + 4zx]
31. Factorise: 125x³ + 8y³ + Z³ – 30xyz. [Answer: (5x + 2y + z)(25x² + 4y² + z² – 10xy – 2yz – 5zx]
32. If x + 2 is a factor of polynomial ax³ + bx² + x – 2 and the remainder 4 is obtained when dividing this polynomial by (x – 2). Find the value of a and b. [Answer: a = 0, b = 2]
33. Check whether p(t) = 6t³ + 3t² + 3t + 18 is a multiple of (2t + 3).
34. A literacy campaign was organised by Class IX students under NSS. Students made (x – 5) rows and (3x – 4) columns, for the rally. (a) Write the total number of students in the form of polynomial. (b) Which values of students are depicted here? [Answer: (a). (x – 5)(3x – 4), (b). Social responsibility]