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Free · Class 9–10 · 9 worksheets · answer keys · practise online · set 12

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 12
Name:Date:Score:    / 10

Write the degree.

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

Value of a polynomial

Class 9 · Worksheet 2 · set 12
Name:Date:Score:    / 8

Find the value.

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

Zero of a polynomial

Class 9 · Worksheet 3 · set 12
Name:Date:Score:    / 8

Answer Yes or No.

  1. Is x = −3 a zero of p(x) = x² + 6x + 8?
  2. Is x = 4 a zero of p(x) = x² + 2x − 24?
  3. Is x = −5 a zero of p(x) = x² + 6x + 8?
  4. Is x = 5 a zero of p(x) = x² + 5x − 6?
  5. Is x = −5 a zero of p(x) = x² + 9x + 20?
  6. Is x = 5 a zero of p(x) = x² − 3x − 10?
  7. Is x = 2 a zero of p(x) = x² + 9x + 18?
  8. Is x = 2 a zero of p(x) = x² − 3x + 2?

Remainder theorem

Class 9 · Worksheet 4 · set 12
Name:Date:Score:    / 8

Find the remainder.

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

Multiply

Class 9 · Worksheet 5 · set 12
Name:Date:Score:    / 10

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

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

Factorise x² + bx + c

Class 9 · Worksheet 6 · set 12
Name:Date:Score:    / 10

Factorise.

  1. x² + x − 20
  2. x² − 3x − 18
  3. x² − 6x − 7
  4. x² + x − 2
  5. x² + 7x + 10
  6. x² − 10x + 24
  7. x² + x − 6
  8. x² + 5x − 24
  9. x² − 3x − 28
  10. x² − 2x − 24

Factorise ax² + bx + c

Class 9–10 · Worksheet 7 · set 12
Name:Date:Score:    / 8

Factorise by splitting the middle term.

  1. 5x² − 28x − 12
  2. 5x² + 27x − 18
  3. 2x² + 13x − 7
  4. 2x² + x − 3
  5. 4x² − 7x + 3
  6. 3x² + 25x + 42
  7. 3x² + 11x + 6
  8. 3x² + 10x + 8

Zeroes of a quadratic

Class 10 · Worksheet 8 · set 12
Name:Date:Score:    / 8

Find the zeroes of each polynomial.

  1. x² − 4x + 3
  2. x² + 9x + 18
  3. x² − 4x − 21
  4. x² + 2x − 15
  5. x² − 3x − 54
  6. x² − x − 20
  7. x² − 12x + 35
  8. x² − 17x + 72

Sum and product of zeroes

Class 10 · Worksheet 9 · set 12
Name:Date:Score:    / 8

Find the sum and the product of the zeroes.

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