CLASS 09 · CHAPTER 02

Polynomials
Practice Questions

20 curated NCERT questions to test your problem-solving skills. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

Which of the following is a polynomial in one variable?

Q2MCQ1 Mark

Degree of the constant polynomial 5 is:

Q3MCQ1 Mark

If p(x) = x³ - 3x² + 2x + 1, then p(-1) is:

Q4MCQ1 Mark

Zero of polynomial p(x) = 2x + 5 is:

Q5Assertion-Reason1 Mark

Assertion (A): x + 1 is a factor of x³ + 1. Reason (R): If p(-a) = 0, then (x + a) is a factor of p(x).

Q6Assertion-Reason1 Mark

Assertion (A): Degree of polynomial x⁵ - x⁴ + 3 is 5. Reason (R): Degree of a polynomial is the highest power of the variable.

Q7Short Answer2 Marks

Find k if x - 1 is factor of 4x³ + 3x² - 4x + k.

Q8Short Answer2 Marks

Evaluate 103 × 107 using identity.

Q9Short Answer2 Marks

Factorise: 4x² + 9y² + 16z² + 12xy - 24yz - 16xz.

Q10Short Answer2 Marks

Find remainder when x³ - ax² + 6x - a is divided by x - a.

Q11Short Answer2 Marks

Factorise 6x² + 17x + 5 by splitting middle term.

Q12Long Answer3 Marks

Factorise: x³ - 23x² + 142x - 120.

Q13Long Answer3 Marks

If x + y + z = 0, show x³ + y³ + z³ = 3xyz.

Q14Long Answer3 Marks

Evaluate (-12)³ + 7³ + 5³ without calculating cubes.

Q15Long Answer3 Marks

Verify: x³ + y³ = (x + y)(x² - xy + y²).

Q16Case Study4 Marks

Case Study Scenario: Volume of container is V(x) = 3x² - 12x. Question: Find possible dimensions.

Q17Case Study4 Marks

Case Study Scenario: Area of rectangular park A(x) = 25a² - 35a + 12. Question: Find length and breadth expressions.

Q18PYQ5 Marks

If x² + 1/x² = 27, find x + 1/x and x³ + 1/x³.

Q19PYQ5 Marks

Find a and b so (x-1) and (x+2) are factors of x³ + ax² + bx - 6.

Q20PYQ5 Marks

Polynomials Practice Questions