CLASS 10 – POLYNOMIALS SAMPLE PAPER (NCERT Based)

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Time: 45 Minutes
Maximum Marks: 40

SECTION A – Very Short Answer Questions (1 Mark Each)

(12 Questions × 1 = 12 Marks)

  1. What is the degree of the polynomial:
    7x3−4x+97x^3 – 4x + 97×3−4x+9
  2. Write the value of the polynomial p(x)=3x−5p(x) = 3x – 5p(x)=3x−5 at x=2x = 2x=2.
  3. If p(x)=x2−4p(x) = x^2 – 4p(x)=x2−4, find p(0)p(0)p(0).
  4. State whether the following is a polynomial or not:
    3x+2\frac{3}{x} + 2x3​+2
  5. What is the coefficient of x2x^2x2 in the polynomial
    4x2−7x+14x^2 – 7x + 14×2−7x+1
  6. Write the degree of the polynomial:
    9x4−7x2+19x^4 – 7x^2 + 19×4−7×2+1
  7. Is 5x−2+35x^{-2} + 35x−2+3 a polynomial? (Yes/No)
  8. Find the value of the polynomial p(x)=x2−3x+2p(x) = x^2 – 3x + 2p(x)=x2−3x+2 at x=1x = 1x=1.
  9. What is the constant term in the polynomial
    4x3−2x+94x^3 – 2x + 94×3−2x+9?
  10. Write the number of terms in the polynomial:
    3x2−5x+73x^2 – 5x + 73×2−5x+7
  11. If zero of p(x)=7x+kp(x) = 7x + kp(x)=7x+k is 3, find the value of k.
  12. Write the degree of:
    5x7−x4+95x^7 – x^4 + 95×7−x4+9

SECTION B – Short Answer Questions (2 Marks Each)

(8 Questions × 2 = 16 Marks)

  1. Find the zero of the linear polynomial
    p(x)=5x−15p(x) = 5x – 15p(x)=5x−15
  2. Verify that 2 is a zero of the polynomial
    p(x)=x2−5x+6p(x) = x^2 – 5x + 6p(x)=x2−5x+6
  3. Divide the polynomial
    2x3+3x2−11x+62x^3 + 3x^2 – 11x + 62×3+3×2−11x+6
    by x−2x – 2x−2
  4. Find the remainder when
    x3−3x2+x+2x^3 – 3x^2 + x + 2x3−3×2+x+2 is divided by x−1x – 1x−1
  5. Find the zeros of the polynomial
    p(x)=x2−9p(x) = x^2 – 9p(x)=x2−9
  6. Check whether 1 is a zero of
    p(x)=x3−2x2+xp(x) = x^3 – 2x^2 + xp(x)=x3−2×2+x
  7. Divide:
    3x3+x2−5x+23x^3 + x^2 – 5x + 23×3+x2−5x+2 by x−1x – 1x−1
  8. Using remainder theorem, find the remainder when
    x3−4x+1x^3 – 4x + 1x3−4x+1 is divided by x+2x + 2x+2

SECTION C – Long Answer Questions (3 Marks Each)

(6 Questions × 3 = 18 Marks)

  1. Using factor theorem, factorise:
    x3−4x2+x+6x^3 – 4x^2 + x + 6x3−4×2+x+6
  2. The polynomial
    p(x)=x3−3x2+x+2p(x) = x^3 – 3x^2 + x + 2p(x)=x3−3×2+x+2
    has one zero at x=−1x = -1x=−1.
    Find the other two zeros.
  3. If a polynomial has zeros 3 and −2,
    form a quadratic polynomial whose zeros are these values.
  4. Factorise using identities:
    x3−8x^3 – 8x3−8
  5. Factorise completely:
    x3+x2−4x−4x^3 + x^2 – 4x – 4x3+x2−4x−4
  6. Use factor theorem to show 2 is a zero of
    p(x)=2x3−5x2−4x+8p(x) = 2x^3 – 5x^2 – 4x + 8p(x)=2×3−5×2−4x+8
    Then find remaining factors.
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