Chapter 2. Polynomials
Exercise 2.3
Solution:
(i)By remainder theorem, the required remainder is equal to p(x) = (-1)
P (-1) = x3+ 3x2+ 3x+1
= (-1)3 + 3 (-1)2 + 3(-1) + 1
= -1 + 3 – 3 + 1 = 0
Required remainder is p (-1) = 0
Required remainder is p (1/2) = 0
(iv) By remainder theorem, the required remainder is equal to p(x) = - π
P(x) = x3+ 3x2+ 3x+1
P(π) = (- π)3 + 3(-π)2 + 3(-π) + 1
= (-π)3 + 3π2 + 3π + 1
Required remainder is p (π) = 0
Required remainder is p (- 5/2) = 0
Q.2. find the remainder when x3- ax2 + 6x - a is divided by x- a.
Solution: Let P(x) = x3- ax2+ 6x- a . P(x) = a.
By remainder theorem
P (a) = (a)3- a(a)2+ 6(a) - a
=a3-a3 + 6a - a
Remainder = 5a
Q3. Check whether 7 + 3x is a factor of 3x3 + 7x.
Solution:
g(x) = 7 + 3x = 0
⇒ 3x = - 7
P(x) ≠ 0
Therefore, 7 + 3x is not a factor of P(x).
