Apps

TalentJR apps

How the apps work →
Free · Class 9–10 · 9 worksheets · answer keys · practise online · set 6

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.

💡 Learn it first

📈 The worksheets

🔄 New set of questions

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 6
Name:Date:Score:    / 10

Write the degree.

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

Value of a polynomial

Class 9 · Worksheet 2 · set 6
Name:Date:Score:    / 8

Find the value.

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

Zero of a polynomial

Class 9 · Worksheet 3 · set 6
Name:Date:Score:    / 8

Answer Yes or No.

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

Remainder theorem

Class 9 · Worksheet 4 · set 6
Name:Date:Score:    / 8

Find the remainder.

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

Multiply

Class 9 · Worksheet 5 · set 6
Name:Date:Score:    / 10

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

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

Factorise x² + bx + c

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

Factorise.

  1. x² − 5x + 6
  2. x² − 10x + 24
  3. x² + 15x + 56
  4. x² + 6x − 7
  5. x² + 3x + 2
  6. x² − 4x + 3
  7. x² − 9x + 18
  8. x² − 14x + 49
  9. x² + 5x + 4
  10. x² + 2x − 24

Factorise ax² + bx + c

Class 9–10 · Worksheet 7 · set 6
Name:Date:Score:    / 8

Factorise by splitting the middle term.

  1. 4x² + 17x − 15
  2. 5x² + 27x − 18
  3. 5x² + 2x − 7
  4. 5x² + 11x + 2
  5. 2x² + 7x + 3
  6. 5x² + 32x + 12
  7. 3x² − 16x + 21
  8. 2x² − x − 10

Zeroes of a quadratic

Class 10 · Worksheet 8 · set 6
Name:Date:Score:    / 8

Find the zeroes of each polynomial.

  1. x² + 12x + 32
  2. x² + 15x + 54
  3. x² − 4x − 45
  4. x² + 2x − 3
  5. x² − 9x + 18
  6. x² − 11x + 24
  7. x² − 3x − 54
  8. x² − x − 2

Sum and product of zeroes

Class 10 · Worksheet 9 · set 6
Name:Date:Score:    / 8

Find the sum and the product of the zeroes.

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

More worksheets

🧮 Algebra formulas sheet📉 Linear equations in two variables🔤 Algebraic expressions Noun worksheetsPronoun worksheetsArticles worksheetTenses worksheetPrepositions worksheetSubtraction worksheets All worksheets

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.

Are these worksheets free?

Yes — print them or save as PDF free. Every worksheet has an answer key.

How do I get different questions?

Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).

How do I print only one worksheet?

Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.

Can my child do this worksheet online, like a quiz?

Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.