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Free · Class 9–10 · 9 worksheets · answer keys · practise online · set 31

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 31
Name:Date:Score:    / 10

Write the degree.

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

Value of a polynomial

Class 9 · Worksheet 2 · set 31
Name:Date:Score:    / 8

Find the value.

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

Zero of a polynomial

Class 9 · Worksheet 3 · set 31
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is x = −5 a zero of p(x) = x² − 2x − 24?
  2. Is x = −4 a zero of p(x) = x² + 4x − 5?
  3. Is x = 6 a zero of p(x) = x² − 12x + 36?
  4. Is x = −6 a zero of p(x) = x² + 5x − 6?
  5. Is x = −6 a zero of p(x) = x² + 7x + 10?
  6. Is x = 1 a zero of p(x) = x² + 5x + 4?
  7. Is x = 2 a zero of p(x) = x² − 4?
  8. Is x = −3 a zero of p(x) = x² + 6x + 9?

Remainder theorem

Class 9 · Worksheet 4 · set 31
Name:Date:Score:    / 8

Find the remainder.

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

Multiply

Class 9 · Worksheet 5 · set 31
Name:Date:Score:    / 10

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

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

Factorise x² + bx + c

Class 9 · Worksheet 6 · set 31
Name:Date:Score:    / 10

Factorise.

  1. x² − 2x − 35
  2. x² + 5x − 36
  3. x² + x − 6
  4. x² + 2x + 1
  5. x² + 4x − 12
  6. x² + 8x − 9
  7. x² − 11x + 18
  8. x² − 10x + 9
  9. x² + 4x + 3
  10. x² + 10x + 21

Factorise ax² + bx + c

Class 9–10 · Worksheet 7 · set 31
Name:Date:Score:    / 8

Factorise by splitting the middle term.

  1. 5x² + 24x − 5
  2. 2x² − 3x − 35
  3. 2x² + 17x + 21
  4. 5x² + 37x + 14
  5. 5x² + 9x − 18
  6. 2x² − 13x − 7
  7. 3x² − 23x + 14
  8. 3x² + 13x + 12

Zeroes of a quadratic

Class 10 · Worksheet 8 · set 31
Name:Date:Score:    / 8

Find the zeroes of each polynomial.

  1. x² + x − 30
  2. x² − 11x + 24
  3. x² + 7x + 12
  4. x² + 17x + 72
  5. x² − 3x − 54
  6. x² − 7x − 18
  7. x² − 7x + 12
  8. x² − 9x + 8

Sum and product of zeroes

Class 10 · Worksheet 9 · set 31
Name:Date:Score:    / 8

Find the sum and the product of the zeroes.

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