← Back to topic
Vidaara.orgClass 10 · Mathematics
CodeVID-M10-14-REM-01
Remainder Theorem — Assignment
Chapter: Factorization
Topic: Remainder Theorem
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The remainder of $p(x)\div(x-a)$ is:
  • A.$p(0)$
  • B.$p(a)$
  • C.$0$
  • D.$a$
2.
The remainder of $p(x)\div(x+a)$ is:
  • A.$p(a)$
  • B.$p(-a)$
  • C.$0$
  • D.$a$
3.
If the remainder is $0$, $(x-a)$ is a:
  • A.root
  • B.factor
  • C.zero
  • D.quotient
4.
The remainder of $x^2\div(x-1)$ is:
  • A.$0$
  • B.$1$
  • C.$2$
  • D.$-1$
5.
The remainder theorem helps avoid:
  • A.addition
  • B.long division
  • C.factoring
  • D.graphing
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the remainder when $x^2+1$ is divided by $(x-2)$.
7.
Find the remainder when $x^3-1$ is divided by $(x-1)$.
8.
Find the remainder of $2x^2-3x+1$ divided by $(x-1)$.
9.
Find the remainder of $x^3+x$ divided by $(x+1)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the remainder when $x^3-3x^2+2x+5$ is divided by $(x-2)$.
11.
Find $k$ if $x^2+kx+6$ leaves remainder $12$ on division by $(x-2)$.
12.
Find the remainder when $4x^3-3x+1$ is divided by $(x+1)$.
13.
If $x^3-2x^2+ax+b$ leaves remainder $0$ at $x=1$, find a relation between $a$ and $b$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $x^3+ax^2+bx-12$ is exactly divisible by $(x-2)$ and $(x+3)$, find $a$ and $b$.
15.
Find $a$ if dividing $ax^3+9x^2+4x-10$ by $(x+3)$ leaves remainder $5$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $p(a)$
  2. (B) $p(-a)$
  3. (B) factor
  4. (B) $1$
  5. (B) long division
Section B — Short Answer (2 marks)
  1. $5$.
  2. $0$.
  3. $0$.
  4. $-2$.
Section C — Short Answer (3 marks)
  1. $5$.
  2. $k=1$.
  3. $0$.
  4. $a+b=1$.
Section D — Long Answer (5 marks)
  1. $a=3,\ b=-4$.
  2. $a=2$.
Generated by Vidaara.org · Assignment VID-M10-14-REM-01 · vidaara.org