Class 9 Maths Polynomials Worksheet — Free Printable PDF
Download a free Class 9 Maths worksheet on Polynomials with MCQs, fill in the blanks and short answer questions. Complete answer key included. Personalized to your class, subject and chapter.
⭐ MeritMate — Class 9 Maths: Polynomials
Curriculum-Aware · meritmate.inSection A: Multiple Choice Questions
Q1. Which of the following is a polynomial?
a) x² + 2x + 1/x
b) √x + 3
c) x³ - 2x² + 5x - 7
d) x^(1/2) + x + 1
Q2. The degree of the polynomial 5x⁴ - 3x² + 2x - 9 is:
a) 2
b) 3
c) 4
d) 9
Q3. If p(x) = x² - 3x + 2, then p(1) is equal to:
a) 0
b) 1
c) 2
d) 6
Q4. Which of the following is a zero of the polynomial p(x) = 2x + 4?
a) 2
b) -2
c) 4
d) -4
Q5. The value of (99)³ using the identity (a - b)³ is:
a) 970299
b) 970399
c) 997002
d) 970229
Section B: Fill in the Blanks
Q6. A polynomial of degree one is called a ________.
Q7. The zero of the polynomial p(x) = 3x - 6 is ________.
Q8. If (x + 1) is a factor of the polynomial p(x) = x³ + kx² + 2x + 3, and p(-1) = 0, then k = ________.
Q9. The expansion of (a + b)³ is ________.
Q10. A polynomial having only one term is called a ________.
Section C: Short Answer Questions
Q11. Find the remainder when p(x) = x³ - 6x² + 11x - 6 is divided by (x - 2) using the remainder theorem.
Q12. Check whether (x + 2) is a factor of the polynomial p(x) = x³ + 3x² + 5x + 6.
Q13. Factorise the polynomial x² + 7x + 12.
Q14. Using a suitable identity, find the value of 102 × 98.
Q15. Write the degree and number of terms of the polynomial p(x) = 4x³ - 3x² + 2x - 5. Also identify the coefficient of x².
⭐ Answer Key
Class 9 · Maths · PolynomialsAnswer Key
Section A: Multiple Choice Questions
Q1. Answer: c) x³ - 2x² + 5x - 7
Explanation: A polynomial must have whole number exponents for the variable. Option c satisfies this condition.
Q2. Answer: c) 4
Explanation: The degree of a polynomial is the highest power of the variable. Here the highest power is 4.
Q3. Answer: a) 0
Explanation: p(1) = (1)² - 3(1) + 2 = 1 - 3 + 2 = 0.
Q4. Answer: b) -2
Explanation: Setting 2x + 4 = 0 gives x = -2.
Q5. Answer: a) 970299
Explanation: (99)³ = (100 - 1)³ = 1000000 - 3(10000) + 3(100) - 1 = 970299.
Section B: Fill in the Blanks
Q6. Linear polynomial
Q7. 2
Explanation: Setting 3x - 6 = 0 gives x = 2.
Q8. k = 4
Explanation: p(-1) = (-1)³ + k(-1)² + 2(-1) + 3 = 0 gives -1 + k - 2 + 3 = 0, so k = 0. Wait, recalculating: -1 + k - 2 + 3 = 0 means k = 0. Answer: k = 0.
Q9. a³ + 3a²b + 3ab² + b³
Q10. Monomial
Section C: Short Answer Questions
Q11. By remainder theorem, substitute x = 2.
p(2) = (2)³ - 6(2)² + 11(2) - 6
p(2) = 8 - 24 + 22 - 6
p(2) = 0
The remainder is 0.
Q12. Substitute x = -2 in p(x).
p(-2) = (-2)³ + 3(-2)² + 5(-2) + 6
p(-2) = -8 + 12 - 10 + 6
p(-2) = 0
Since p(-2) = 0, (x + 2) is a factor of p(x).
Q13. We need two numbers whose product is 12 and sum is 7. Those numbers are 3 and 4.
x² + 7x + 12 = x² + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 3)(x + 4)
Q14. 102 × 98 = (100 + 2)(100 - 2)
Using identity (a + b)(a - b) = a² - b²:
= (100)² - (2)²
= 10000 - 4
= 9996
Q15. The polynomial is p(x) = 4x³ - 3x² + 2x - 5.
Degree: 3 (highest power of x is 3).
Number of terms: 4 (the terms are 4x³, -3x², 2x, and -5).
Coefficient of x²: -3.
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