NCERT Solutions For Class 9 Math Chapter – 2 Exercise – 2.3
Q1. Find the remainder when x3 + 3x2 + 3x + 1 is divided by
- X + 1
Solution:-
X + 1 = 0
X = -1
Remainder
P(-1) = (-1)3 + 3(-1)2 + 3(-1) + 1
= -1 + 3 – 3 + 1
= 0
- X – 1/2
Solution:-
X – 1/2 = 0
X = 1/2
Remainder
P(1/2) = (1/2)3 + 3(1/2)2 + 3(1/2) + 1
= (1/8) + (3/4) + (3/2) + 1
= 27/8
- X
Solution:-
X = 0
Remainder:
P(0) = (0)3 + 3(0) + 1
= 1
- X + ∏
Solution:-
X + ∏ = 0
X = -∏
Remainder
p(0) = (-∏)3 + 3(-∏)2 + 3(-∏) + 1
= -∏3 + 3∏ + 1
- 5 + 2x
Solution:-
5 + 2x = 0
X = -5/2
Remainder
(-5/2)3 + 3(-5/2)2 + 3(-5/2) + 1
= -27/8
Q2. Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Solution:-
X – a = 0
X = a
Remainder
P(a) = (a)3 – a(a2) + 6(a) – a
= a3 – a3 + 6a – a
= 5a
Q3. Check whether 7 + 3x is a factor of 3x3 + 7x.
Solution:-
7 + 3x = 0
3x = – 7
X = -7/3
Remainder:
3(-7/3)3 + 7(-7/3) =-(343/9) + (-49/3)
= (-343 – (49)3)/9
= -490/9 ≠ 0