Class 9 Mathematics · Chapter 4 · Test 2
Cubic and quadratic analysis
40 MCQs
40 questions · 35 min · 40 marks
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Sample questions
The first 5 of 40. Try each one, then tap to see the answer.
Question 1
The factorization of a⁴ + a²b² + b⁴ is:
- A(a² + ab + b²)²
- B(a² − ab + b²)(a² + ab + b²)
- C(a² − b²)(a² + b²)
- D(a − b)²(a + b)²
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Answer: B
(a² + b²)² − (ab)² = (a² − ab + b²)(a² + ab + b²).
Question 2
To factorize a⁴ + a²b² + b⁴ the term added and subtracted is:
- Aa²b²
- B4a²b²
- Cab
- D2a²b²
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Answer: D
Adding and subtracting 2a²b² creates the perfect square (a² + b²)².
Question 3
a⁴ + a²b² + b⁴ is rewritten as the difference of squares:
- A(a² + b²)² − (ab)²
- B(a² − b²)² − (ab)²
- C(a² + b²)² − (2ab)²
- D(a² + b²)² + (ab)²
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Answer: A
a⁴ + 2a²b² + b⁴ − a²b² = (a² + b²)² − (ab)².
Question 4
Factorize x⁴ + x² + 25:
- A(x² + 3x + 5)²
- B(x² − 5)(x² + 5)
- C(x² − 3x + 5)(x² + 3x + 5)
- D(x² − x + 5)(x² + x + 5)
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Answer: C
(x² + 5)² − (3x)² = (x² − 3x + 5)(x² + 3x + 5).
Question 5
Factorize x⁴ + 4:
- A(x² − 2)(x² + 2)
- B(x² − 2x + 2)(x² + 2x + 2)
- C(x² + 2x + 2)²
- D(x² − 4x + 2)(x² + 4x + 2)
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Answer: B
(x² + 2)² − (2x)² = (x² − 2x + 2)(x² + 2x + 2).
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