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Free · Class 9–10 · 9 worksheets · answer keys · practise online · set 37

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 37
Name:Date:Score:    / 10

Write the degree.

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

Value of a polynomial

Class 9 · Worksheet 2 · set 37
Name:Date:Score:    / 8

Find the value.

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

Zero of a polynomial

Class 9 · Worksheet 3 · set 37
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is x = −4 a zero of p(x) = x² − 10x + 24?
  2. Is x = 4 a zero of p(x) = x² − 9x + 20?
  3. Is x = −2 a zero of p(x) = x² + 8x + 12?
  4. Is x = −4 a zero of p(x) = x² + 2x − 8?
  5. Is x = 4 a zero of p(x) = x² + x − 20?
  6. Is x = 2 a zero of p(x) = x² − x − 2?
  7. Is x = −5 a zero of p(x) = x² + 6x + 8?
  8. Is x = 6 a zero of p(x) = x² − 16?

Remainder theorem

Class 9 · Worksheet 4 · set 37
Name:Date:Score:    / 8

Find the remainder.

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

Multiply

Class 9 · Worksheet 5 · set 37
Name:Date:Score:    / 10

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

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

Factorise x² + bx + c

Class 9 · Worksheet 6 · set 37
Name:Date:Score:    / 10

Factorise.

  1. x² + 2x − 3
  2. x² + 8x + 12
  3. x² − 3x − 28
  4. x² + 15x + 54
  5. x² − 5x − 14
  6. x² − 8x − 9
  7. x² + 7x + 6
  8. x² + 2x − 35
  9. x² + 4x − 5
  10. x² − 11x + 18

Factorise ax² + bx + c

Class 9–10 · Worksheet 7 · set 37
Name:Date:Score:    / 8

Factorise by splitting the middle term.

  1. 5x² + 27x − 18
  2. 4x² − 11x + 7
  3. 2x² − 17x + 21
  4. 2x² − 3x − 14
  5. 2x² − 11x + 15
  6. 2x² + 15x + 18
  7. 5x² − 34x − 7
  8. 2x² + 3x − 5

Zeroes of a quadratic

Class 10 · Worksheet 8 · set 37
Name:Date:Score:    / 8

Find the zeroes of each polynomial.

  1. x² + 10x + 21
  2. x² − 5x − 6
  3. x² + 8x + 15
  4. x² − 4x − 45
  5. x² + 5x − 36
  6. x² − x − 6
  7. x² − 7x + 12
  8. x² + 14x + 48

Sum and product of zeroes

Class 10 · Worksheet 9 · set 37
Name:Date:Score:    / 8

Find the sum and the product of the zeroes.

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

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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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