Remainder/factor theorems, factorisation, identities MCQs
Practice Remainder/factor theorems, factorisation, identities multiple-choice questions from Polynomials (Class 9 Maths) - tap an answer for instant feedback and a step-by-step solution. Practice the full set free on the RankByte app.
Remainder/factor theorems, factorisation, identitiesQuiz - Solve & Score
Q1. Which is a factor of 64x³ − 1?
- A.4x − 1
- B.4x + 1
- C.8x − 1
- D.2x − 1
Answer: A. 4x − 1
Given 64, 1, asked for the unknown. By a³ − b³ with a = 4x, b = 1: 64x³ − 1 = (4x − 1)(16x² + 4x + 1). a³ − b³ with a = 4x, b = 1: 64x³ − 1 = (4x − 1)(16x² + 4x + 1). Thus option A) 4x − 1.
Q2. Value of 1² + 2² + … + 10² (using n(n+1)(2n+1)/6) is
- A.385
- B.375
- C.395
- D.405
Answer: A. 385
Start by listing the data - 1, 2, 10, 1, 2 (math, chapter 'Polynomials'). What we must find: the requested quantity. The relevant chapter relation links the data to the unknown - rearrange it to isolate the quantity we are solving for. Crunching it out: 10·11·21/6 = 385. So the correct choice is A) 385.
Q3. If p(x) = x³ + 2x² − x − 2 has x = 1 as a zero, the factorisation is
- A.(x − 1)(x + 1)(x + 2)
- B.(x − 1)(x − 2)(x + 1)
- C.(x + 1)(x + 2)(x − 2)
- D.(x − 1)²(x + 2)
Answer: A. (x − 1)(x + 1)(x + 2)
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