Vidaara.orgClass 9 · Mathematics
CodeVID-M09-02-REM-01
Division & Remainder Theorem — Assignment
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.
$(x-a)$ is a factor iff:
- A.$p(a)=1$
- B.$p(a)=0$
- C.$p(0)=a$
- D.$a=0$
3.
The remainder of $x^2+1$ by $(x-1)$ is:
- A.$0$
- B.$1$
- C.$2$
- D.$-1$
4.
Division algorithm: dividend $=$ divisor $\times$ quotient $+$:
- A.remainder
- B.dividend
- C.zero
- D.quotient
5.
If $p(2)=0$, a factor of $p(x)$ is:
- A.$(x+2)$
- B.$(x-2)$
- C.$2x$
- D.$(x-1)$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the remainder of $x^2-5x+6$ by $(x-2)$.
7.
Find $p(1)$ for $p(x)=x^3-1$.
8.
Is $(x-1)$ a factor of $x^2-1$?
9.
Find the remainder of $x^3+1$ by $(x+1)$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the remainder when $x^3-3x^2+4x-4$ is divided by $(x-2)$.
11.
Find $k$ if $(x-1)$ is a factor of $x^2+kx-2$.
12.
Find the remainder when $4x^3-3x+2$ is divided by $(x+2)$.
13.
Find the remainder of $x^3+2x^2-x+1$ by $(x-1)$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find $a$ and $b$ if $(x-1)$ and $(x+1)$ are factors of $x^3+ax^2+bx-1$.
15.
Show that $(x-2)$ is a factor of $x^3-4x^2+x+6$ and find the other factors.
Answer Key
Section A — Multiple Choice Questions
- (B) $p(a)$
- (B) $p(a)=0$
- (C) $2$
- (A) remainder
- (B) $(x-2)$
Section B — Short Answer (2 marks)
- $0$.
- $0$.
- Yes.
- $0$.
Section C — Short Answer (3 marks)
- $0$.
- $k=1$.
- $-24$.
- $3$.
Section D — Long Answer (5 marks)
- $a=1,\ b=-1$.
- $(x-2)(x-3)(x+1)$.
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