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CBSE Class 9  >  Class 9 Test  >  Online MCQ Tests  >  Test: Remainder Theorem (Old Syllabus) - Class 9 MCQ

Remainder Theorem (Old Syllabus) - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Remainder Theorem (Old Syllabus) (15 Questions)

You can prepare effectively for Class 9 Online MCQ Tests for Class 9 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Remainder Theorem (Old Syllabus)". These 15 questions have been designed by the experts with the latest curriculum of Class 9 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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Test: Remainder Theorem (Old Syllabus) - Question 1
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If x² - 7x + a has a remainder 1 when divided by x + 1, then

Test: Remainder Theorem (Old Syllabus) - Question 2
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The remainder when the polynomial p(x) = x3 -3x2 +2x-1 is divided by x-2 is

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Test: Remainder Theorem (Old Syllabus) - Question 3
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What is remainder when x3 – 2x2 + x + 1 is divided by (x -1)?

Test: Remainder Theorem (Old Syllabus) - Question 4
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The remainder when x4 – 3x2 + 5x – 7 is divided by x + 1 is:

Detailed Solution: Question 4

Correct Answer :- a

Explanation : x + 1 = 0

x = -1

x4 – 3x2 + 5x – 7

(-1)4 - 3(-1)2 + 5(-1) - 7 = 0

1 - 3 - 5 - 7 

= -14

Test: Remainder Theorem (Old Syllabus) - Question 5
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If x² - 7x + a has a remainder 1 when divided by x + 1, then

Test: Remainder Theorem (Old Syllabus) - Question 6
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The remainder when x3 + x2 - 2x +1 is divided by (x+1) is

Detailed Solution: Question 6

for finding the remainder we need to use remainder theorom

let p(x)=x3+x2-2x+1

Here, the divisor is x+1 for dividend p(x), we need to equate it to 0 and put that value of x in p(x).

−x+1=0

∴x=−1

p(−1)=(-1)3+(−1)2-2(−1)+1=3

Hence, remainder=3

Test: Remainder Theorem (Old Syllabus) - Question 7
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For a polynomial p(x) = 2x4 - 3x3 + 2x2 + 2x-1 what is the remainder when it’s divided by x+4?

Test: Remainder Theorem (Old Syllabus) - Question 8
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Find remainder when x3+1 is divided by x+1

Test: Remainder Theorem (Old Syllabus) - Question 9
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Using Remainder theorem, find the remainder when 3x4 - 4x3 - 3x - 1 by x - 1

Detailed Solution: Question 9

By remainder theorem if x-1 = 0 then x=1 using it in equation we get p(x)= 3x⁴-4x³-3x-1 p(1)= 3x1⁴-4x1³-3x1-1 p(1)= 3-4-3-1 p(1)= -5

Test: Remainder Theorem (Old Syllabus) - Question 10
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In the division of a cubic polynomial p(x) by a linear polynomial, the remainder is p(-2).So, the divisor must be

Test: Remainder Theorem (Old Syllabus) - Question 11
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If x³ + 9x +5 is divided by x, then remainder is

Test: Remainder Theorem (Old Syllabus) - Question 12
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Find the remainder when P(x) = x2 - 2x is divided by x - 2

Test: Remainder Theorem (Old Syllabus) - Question 13
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Find p(1/3) for p(t) = t2 – t + 2

Detailed Solution: Question 13

1/9-1/3+2 =1/9-3/9-18/9 =16/9

Test: Remainder Theorem (Old Syllabus) - Question 14
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Using Remainder Theorem find the remainder when x3 - x2 + x - 1 is divided by x - 1

Test: Remainder Theorem (Old Syllabus) - Question 15
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P(x) is a polynomial in x, ‘a’ is a real number. If (x-a) is a factor of p(x), then p (a) must be​

Detailed Solution: Question 15

 If p(x) is a polynomial of degree n which is greater than or equal to one and a is any real number which will be the divisor, then there will be two conditions fulfilled: If p (a) =0, then x-a is a factor of that polynomial p(x). x-a would be the factor of the polynomial if the r(x) i.e. remainder is 0.

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About this Class 9 Practice Test

This test contains 15 MCQs on Remainder Theorem (Old Syllabus) with detailed solutions for each question. It is part of the Online MCQ Tests for Class 9 course on EduRev, designed to align with the current Class 9 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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