1. What is the degree of 4x⁵ − 2x³ + x − 7?
- A5
- B4
- C3
- D13
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Answer: A) 5
Degree = highest power of variable. Here it's 5 (from x⁵).
Class 9 Polynomials — practice questions with answers
Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Factorise x² − 9 using the identity a² − b² = (a + b)(a − b).
- A(x − 3)²
- B(x + 3)(x − 3)
- C(x + 9)(x − 1)
- D(x − 9)(x + 1)
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Answer: B) (x + 3)(x − 3)
x² − 9 = x² − 3² = (x + 3)(x − 3).
3. Without dividing, find the remainder when p(x) = x³ + 1 is divided by (x + 1).
- A1
- B-1
- C2
- D0
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Answer: D) 0
(x + 1) → x = −1. p(−1) = (−1)³ + 1 = −1 + 1 = 0. The remainder is 0, so (x + 1) is a factor.
4. Use the identity for a³ + b³ + c³ − 3abc to evaluate 2³ + 3³ + 4³ − 3(2)(3)(4).
- A99
- B72
- C9
- D27
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Answer: D) 27
The identity gives (a + b + c)(a² + b² + c² − ab − bc − ca) = (2 + 3 + 4)(4 + 9 + 16 − 6 − 12 − 8) = 9 × 3 = 27. Direct check: 8 + 27 + 64 − 72 = 99 − 72 = 27.
5. To factorise x² + 5x − 14 by splitting the middle term, which pair of numbers should 5x be split into?
- A−7 and 2
- B7 and −2
- C7 and 2
- D14 and −1
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Answer: B) 7 and −2
The pair must multiply to −14 (the constant term) and add to +5 (the coefficient of x): 7 × (−2) = −14 and 7 + (−2) = 5. So x² + 7x − 2x − 14 = x(x + 7) − 2(x + 7) = (x + 7)(x − 2). The pair −7 and 2 adds to −5, giving the wrong middle term.
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