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Free · Class 9–10 · 9 worksheets · answer keys · practise online · set 9

Polynomials worksheets — Class 9 and 10, with answers

Free polynomials worksheets for Class 9 and 10: degree, value of a polynomial, zeroes, remainder theorem, multiplying and factorising quadratics, and sum and product of zeroes — with answers.

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Degree of a polynomial (Class 9)Value of a polynomial (Class 9)Zero of a polynomial (Class 9)Remainder theorem (Class 9)Multiply (Class 9)Factorise x² + bx + c (Class 9)Factorise ax² + bx + c (Class 9–10)Zeroes of a quadratic (Class 10)Sum and product of zeroes (Class 10)

Degree of a polynomial

Class 9 · Worksheet 1 · set 9
Name:Date:Score:    / 10

Write the degree.

  1. Degree of −7x⁴ + 8x³ − 4
  2. Degree of 3x³ + x + 4
  3. Degree of −x³ − 9x² − 8
  4. Degree of −5x² − x + 7
  5. Degree of 2x⁶ + 8x⁵ − 7x³ − 9x − 4
  6. Degree of 5x⁴ − 7x³ − 7x² − 8
  7. Degree of −2x³ + 8x² + 7x
  8. Degree of −7x + 3
  9. Degree of x⁶ + 5x⁴ + 9x³ − 3x²
  10. Degree of 2x − 8

Value of a polynomial

Class 9 · Worksheet 2 · set 9
Name:Date:Score:    / 8

Find the value.

  1. p(x) = 2x² − 9x − 7. Find p(−1).
  2. p(x) = x² − 8. Find p(0).
  3. p(x) = −2x² − 5x − 8. Find p(−1).
  4. p(x) = −x² + 5x − 4. Find p(−3).
  5. p(x) = −x² − 9x + 9. Find p(−2).
  6. p(x) = −4x² − 5x − 7. Find p(−3).
  7. p(x) = 2x² + x + 7. Find p(0).
  8. p(x) = 2x² − 6x − 4. Find p(−3).

Zero of a polynomial

Class 9 · Worksheet 3 · set 9
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is x = −4 a zero of p(x) = x² + 2x − 8?
  2. Is x = −2 a zero of p(x) = x² − 2x − 24?
  3. Is x = 2 a zero of p(x) = x² + 2x − 8?
  4. Is x = −5 a zero of p(x) = x² + x − 20?
  5. Is x = 4 a zero of p(x) = x² − 7x + 6?
  6. Is x = 5 a zero of p(x) = x² − 2x − 15?
  7. Is x = 1 a zero of p(x) = x² + 4x − 5?
  8. Is x = −3 a zero of p(x) = x² + 8x + 15?

Remainder theorem

Class 9 · Worksheet 4 · set 9
Name:Date:Score:    / 8

Find the remainder.

  1. Remainder when 4x³ + 6x² − 5x + 3 is divided by (x + 3)
  2. Remainder when x³ + 3x² − 2x − 8 is divided by (x + 2)
  3. Remainder when 2x³ + 5x² − 4x − 6 is divided by (x − 1)
  4. Remainder when 4x³ − 2x² − 5x + 1 is divided by (x + 1)
  5. Remainder when x³ − x² + 3x + 4 is divided by (x + 2)
  6. Remainder when 4x³ − 6x² + 4x + 5 is divided by (x − 3)
  7. Remainder when 3x³ + 4x² − 4x + 8 is divided by (x − 2)
  8. Remainder when x³ − x² − 7x + 7 is divided by (x + 3)

Multiply

Class 9 · Worksheet 5 · set 9
Name:Date:Score:    / 10

Multiply using (x + a)(x + b) = x² + (a + b)x + ab.

  1. (x − 6)(x + 2)
  2. (x + 2)(x − 6)
  3. (x − 9)(x − 3)
  4. (x + 6)(x + 5)
  5. (x + 1)(x + 4)
  6. (x − 8)(x − 2)
  7. (x + 3)(x − 3)
  8. (x − 9)(x − 6)
  9. (x + 1)(x + 2)
  10. (x + 4)(x − 3)

Factorise x² + bx + c

Class 9 · Worksheet 6 · set 9
Name:Date:Score:    / 10

Factorise.

  1. x² + 6x + 5
  2. x² + 12x + 36
  3. x² + 6x − 7
  4. x² + 8x + 7
  5. x² + 9x + 8
  6. x² − 6x + 8
  7. x² − 8x − 9
  8. x² + 17x + 72
  9. x² − 10x + 25
  10. x² + 8x − 9

Factorise ax² + bx + c

Class 9–10 · Worksheet 7 · set 9
Name:Date:Score:    / 8

Factorise by splitting the middle term.

  1. 3x² + x − 2
  2. 5x² − 3x − 14
  3. 4x² − x − 5
  4. 5x² + 38x + 21
  5. 5x² + 42x + 49
  6. 2x² − x − 1
  7. 3x² + 8x − 35
  8. 4x² − 9x − 28

Zeroes of a quadratic

Class 10 · Worksheet 8 · set 9
Name:Date:Score:    / 8

Find the zeroes of each polynomial.

  1. x² − 7x + 6
  2. x² − 11x + 24
  3. x² − x − 20
  4. x² − 2x − 3
  5. x² − 6x − 7
  6. x² − 13x + 42
  7. x² − 3x − 40
  8. x² + 4x + 3

Sum and product of zeroes

Class 10 · Worksheet 9 · set 9
Name:Date:Score:    / 8

Find the sum and the product of the zeroes.

  1. Sum and product of the zeroes of x² + x − 12
  2. Sum and product of the zeroes of x² + 4x + 10
  3. Sum and product of the zeroes of 2x² − 9x + 4
  4. Sum and product of the zeroes of x² + 10x + 8
  5. Sum and product of the zeroes of 5x² + 10x − 7
  6. Sum and product of the zeroes of 5x² − 7x + 1
  7. Sum and product of the zeroes of 6x² − 11x + 9
  8. Sum and product of the zeroes of 6x² + 3x − 12

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Questions

What is the zero of a polynomial?

A value of x that makes the polynomial equal to 0. For x² − 5x + 6 = (x − 2)(x − 3), the zeroes are 2 and 3.

What is the remainder theorem?

When p(x) is divided by (x − a), the remainder is p(a) — so you can find the remainder without long division.

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