Vidaara.orgClass 10 · Mathematics
CodeVID-M10-14-CUB-01
Factorisation of Cubic Polynomials — 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.
To factorise a cubic, first use the:
- A.quadratic formula
- B.factor theorem
- C.binomial theorem
- D.graph
2.
A cubic has at most:
- A.$1$ factor
- B.$2$ factors
- C.$3$ linear factors
- D.$4$ factors
3.
After one factor, divide to get a:
- A.linear
- B.quadratic
- C.cubic
- D.constant
4.
$x^3-1=$
- A.$(x-1)(x^2+x+1)$
- B.$(x-1)^3$
- C.$(x-1)(x+1)$
- D.$(x+1)^3$
5.
A cubic has at least how many real roots?
- A.$0$
- B.$1$
- C.$2$
- D.$3$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Factorise $x^3-1$.
7.
Factorise $x^3+8$.
8.
Given $(x-1)$ is a factor of $x^3-6x^2+11x-6$, find the other factors.
9.
Factorise $x^3-x$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Factorise $x^3-3x^2-x+3$.
11.
Factorise $x^3+2x^2-x-2$.
12.
Factorise $2x^3-3x^2-3x+2$.
13.
Factorise $x^3-7x+6$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Factorise completely: $x^3-6x^2+11x-6$.
15.
Factorise completely: $x^3+6x^2+11x+6$.
Answer Key
Section A — Multiple Choice Questions
- (B) factor theorem
- (C) $3$ linear factors
- (B) quadratic
- (A) $(x-1)(x^2+x+1)$
- (B) $1$
Section B — Short Answer (2 marks)
- $(x-1)(x^2+x+1)$.
- $(x+2)(x^2-2x+4)$.
- $(x-2)(x-3)$.
- $x(x-1)(x+1)$.
Section C — Short Answer (3 marks)
- $(x-1)(x+1)(x-3)$.
- $(x-1)(x+1)(x+2)$.
- $(x-2)(x+1)(2x-1)$.
- $(x-1)(x-2)(x+3)$.
Section D — Long Answer (5 marks)
- $(x-1)(x-2)(x-3)$.
- $(x+1)(x+2)(x+3)$.
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