Remainder Theorem MCQs
Practice Remainder Theorem 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 TheoremQuiz - Solve & Score
Q1. A potter glazing a bowl for the kiln describes the load by p(x) = 3x^2 - 3x + 4. When the parameter is moved to x = 4, what value does the remainder on dividing p(x) by (x - 4) equal?
- A.32
- B.40
- C.36
- D.64
Answer: B. 40
By the Remainder Theorem the remainder on dividing by (x - 4) is p(4). Substitute: p(4) = 3x^2 - 3x + 4. Compute term by term: 3*(4)^2 - 3*(4) + 4 = 40.
Q2. A bridge inspector reading a strain gauge models the system by p(x) = 2x^3 + 2x^2 - 3. What remainder results when p(x) is divided by (x + 1)?
- A.1
- B.0
- C.-1
- D.-3
Answer: D. -3
Remainder on division by (x + 1) equals p(-1). p(-1) = 2*(-1)^3 + 2*(-1)^2 - 3 = -3.
Q3. A video-game physics coder sets the model p(x) = 2x^2 + 4x - 3 and divides it by (3x - -3). What remainder is produced?
- A.-5
- B.-4
- C.3
- D.27
Answer: A. -5
Set the divisor to zero: 3x - -3 = 0 gives x = -1. The remainder is p(-1) = 2*(-1)^2 + 4*(-1) - 3 = -5.
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