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Gyaan Maths
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CBSE Maths · Class 9

Chapter 2: Polynomials

Name: ________________________
Date: ______________
Marks: ____ / 10

Degree, zeroes, Remainder theorem, Factor theorem, algebraic identities and factorisation.

Questions

  1. p(x)=5x−4x2+3p(x) = 5x - 4x^2 + 3; p(2)p(2).
  2. Evaluate 105×106105\times 106 by identity.
  3. Factorise x2+8x+15x^2 + 8x + 15.
  4. Remainder of (x4+x3−2x2+x+1)÷(x−1)(x^4+x^3-2x^2+x+1)\div (x-1).
  5. Expand (3x−2y)3(3x-2y)^3.
  6. If x+1/x=5x + 1/x = 5, find x2+1/x2x^2 + 1/x^2.
  7. Factorise 6x2+11x+36x^2 + 11x + 3.
  8. Show (x−1)(x-1) is a factor of x3−6x2+11x−6x^3 - 6x^2 + 11x - 6.
  9. Expand (2a+3b+5c)2(2a + 3b + 5c)^2.
  10. If a+b+c=0a + b + c = 0, evaluate a3+b3+c3a^3 + b^3 + c^3.

Extra Practice (Optional)

  • Factorise x3−27x^3 - 27.
  • Evaluate 99299^2 using identity.
  • Expand (x+2y−z)2(x + 2y - z)^2.
  • Factorise x3+3x2−4x−12x^3 + 3x^2 - 4x - 12 (grouping).
  • Value of 1033103^3 using identity.

Answer Key (For Teachers)

  1. Answer: −3-3.
    Working: =10−16+3= 10 - 16 + 3.
  2. Answer: 1113011130.
    Working: (x+a)(x+b)(x+a)(x+b) pattern.
  3. Answer: (x+3)(x+5)(x+3)(x+5).
    Working: Split middle: (x+3)(x+5)(x+3)(x+5).
  4. Answer: 22.
    Working: p(1)=2p(1) = 2.
  5. Answer: 27x3−54x2y+36xy2−8y327x^3-54x^2y+36xy^2-8y^3.
    Working: Use (a−b)3(a-b)^3 identity.
  6. Answer: 2323.
    Working: Square x+1/xx + 1/x.
  7. Answer: (2x+3)(3x+1)(2x+3)(3x+1).
    Working: Product 1818, sum 1111; 9+29+2; (2x+3)(3x+1)(2x+3)(3x+1).
  8. Answer: Yes; factor is (x−1)(x-1).
    Working: p(1)=1−6+11−6=0p(1) = 1 - 6 + 11 - 6 = 0.
  9. Answer: 4a2+9b2+25c2+12ab+30bc+20ca4a^2 + 9b^2 + 25c^2 + 12ab + 30bc + 20ca.
    Working: Use (a+b+c)2(a+b+c)^2: 4a2+9b2+25c2+12ab+30bc+20ca4a^2 + 9b^2 + 25c^2 + 12ab + 30bc + 20ca.
  10. Answer: 3abc3abc.
    Working: Identity gives 3abc3abc.
Gyaan Maths · CBSE Class 9 · Chapter 2
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026