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Free · Class 9–10 · 9 worksheets · answer keys · practise online · set 82

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 82
Name:Date:Score:    / 10

Write the degree.

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

Value of a polynomial

Class 9 · Worksheet 2 · set 82
Name:Date:Score:    / 8

Find the value.

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

Zero of a polynomial

Class 9 · Worksheet 3 · set 82
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is x = 1 a zero of p(x) = x² − 4x + 3?
  2. Is x = −2 a zero of p(x) = x² + 2x − 3?
  3. Is x = 2 a zero of p(x) = x² − 4x + 4?
  4. Is x = 2 a zero of p(x) = x² − 7x + 10?
  5. Is x = −4 a zero of p(x) = x² − x − 20?
  6. Is x = 2 a zero of p(x) = x² + 3x − 10?
  7. Is x = −2 a zero of p(x) = x² − 10x + 24?
  8. Is x = 3 a zero of p(x) = x² − 4x + 3?

Remainder theorem

Class 9 · Worksheet 4 · set 82
Name:Date:Score:    / 8

Find the remainder.

  1. Remainder when 4x³ + 5x² − 5x + 2 is divided by (x − 2)
  2. Remainder when 2x³ − 3x² + 2x − 2 is divided by (x + 3)
  3. Remainder when x³ + x² − 3x − 3 is divided by (x + 3)
  4. Remainder when 3x³ − 6x² + 9x − 3 is divided by (x + 2)
  5. Remainder when 3x³ + x² − 5x + 5 is divided by (x − 3)
  6. Remainder when x³ − 5x² − 9x + 3 is divided by (x − 3)
  7. Remainder when x³ + 3x² + 8x + 7 is divided by (x − 3)
  8. Remainder when x³ + 4x² − 6x + 1 is divided by (x + 2)

Multiply

Class 9 · Worksheet 5 · set 82
Name:Date:Score:    / 10

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

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

Factorise x² + bx + c

Class 9 · Worksheet 6 · set 82
Name:Date:Score:    / 10

Factorise.

  1. x² + 4x − 32
  2. x² + x − 56
  3. x² + 13x + 40
  4. x² + 3x + 2
  5. x² + 9x + 8
  6. x² − 6x − 16
  7. x² − 5x − 24
  8. x² − 11x + 28
  9. x² − 8x + 15
  10. x² + 9x + 20

Factorise ax² + bx + c

Class 9–10 · Worksheet 7 · set 82
Name:Date:Score:    / 8

Factorise by splitting the middle term.

  1. 4x² − 21x − 18
  2. 2x² + 19x + 35
  3. 5x² + x − 6
  4. 3x² − 10x + 7
  5. 2x² − 5x − 12
  6. 3x² − 19x + 28
  7. 5x² − 9x + 4
  8. 4x² − 25x + 6

Zeroes of a quadratic

Class 10 · Worksheet 8 · set 82
Name:Date:Score:    / 8

Find the zeroes of each polynomial.

  1. x² + 4x − 21
  2. x² − 9x + 14
  3. x² − x − 2
  4. x² − 4x − 21
  5. x² − 5x − 24
  6. x² − 15x + 54
  7. x² − 7x + 6
  8. x² − 4x − 45

Sum and product of zeroes

Class 10 · Worksheet 9 · set 82
Name:Date:Score:    / 8

Find the sum and the product of the zeroes.

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

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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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