Question Paper
Class / Subject: Class 10 (ICSE) · Mathematics
Chapter: Chapter 8 — Chapter 8: Remainder and Factor Theorems
Time Allowed: 32 minutes
Max Marks: 16
1. What does the Remainder Theorem state? [1]
(A) Remainder of p(x)÷(x-a) equals p(a)
(B) Remainder is always zero
(C) p(x) has no remainder ever
(D) Nothing specific
2. What does the Factor Theorem state? [1]
(A) (x-a) is a factor if p(a)=0
(B) (x-a) is always a factor
(C) p(a) is always zero
(D) Nothing specific
3. If p(2)=0, what can we conclude? [1]
(A) (x-2) is a factor of p(x)
(B) (x+2) is a factor
(C) p(x) has no factors
(D) Nothing can be concluded
4. What is the remainder when p(x)=x²+2x+1 is divided by (x-1)? [1]
(A) p(1)=4
(B) p(1)=0
(C) p(1)=1
(D) p(1)=2
5. Why use these theorems? [1]
(A) To find factors without long division
(B) To make division harder
(C) No reason
(D) Only for tests
6. What do these theorems help with? [1]
(A) Factorising higher-degree polynomials
(B) Only linear equations
(C) Only quadratic equations
(D) Nothing useful
7. If p(3)=0 for p(x), what factor exists? [1]
(A) (x-3)
(B) (x+3)
(C) (x-1)
(D) No factor exists
8. Why learn the Remainder and Factor Theorems? [1]
(A) Essential for polynomial factorisation
(B) No reason
(C) It's not useful
(D) Only for tests
9. What does the Remainder Theorem state? [1]
(A) Remainder of p(x)÷(x-a) equals p(a)
(B) Remainder is always zero
(C) p(x) has no remainder ever
(D) Nothing specific
10. What does the Factor Theorem state? [1]
(A) (x-a) is a factor if p(a)=0
(B) (x-a) is always a factor
(C) p(a) is always zero
(D) Nothing specific
11. If p(2)=0, what can we conclude? [1]
(A) (x-2) is a factor of p(x)
(B) (x+2) is a factor
(C) p(x) has no factors
(D) Nothing can be concluded
12. What is the remainder when p(x)=x²+2x+1 is divided by (x-1)? [1]
(A) p(1)=4
(B) p(1)=0
(C) p(1)=1
(D) p(1)=2
13. Why use these theorems? [1]
(A) To find factors without long division
(B) To make division harder
(C) No reason
(D) Only for tests
14. What do these theorems help with? [1]
(A) Factorising higher-degree polynomials
(B) Only linear equations
(C) Only quadratic equations
(D) Nothing useful
15. If p(3)=0 for p(x), what factor exists? [1]
(A) (x-3)
(B) (x+3)
(C) (x-1)
(D) No factor exists
16. Why learn the Remainder and Factor Theorems? [1]
(A) Essential for polynomial factorisation
(B) No reason
(C) It's not useful
(D) Only for tests