Thursday, July 29, 2010

Exercise 2.3


Question 1:
Find the remainder when x3 + 3x2 + 3x + 1 is divided by
(i) x + 1 (ii) (iii) x
(iv) x + π (v) 5 + 2x

Ans.
(i) x + 1
By long division,
Therefore, the remainder is 0.
(ii)
By long division,
Therefore, the remainder is.
(iii) x
By long division,
Therefore, the remainder is 1.
(iv) x + π
By long division,
Therefore, the remainder is 
(v) 5 + 2x
By long division,
Therefore, the remainder is

Question 2:
Find the remainder when x3 − ax2 + 6x − is divided by x − a.

Ans.
By long division,
Therefore, when x3 − ax2 + 6x − is divided by x − a, the remainder obtained is 5a.

Question 3:
Check whether 7 + 3x is a factor of 3x3 + 7x.

Ans.
Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3will be a factor of 3x3 + 7x.
By long division,
As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x3 + 7x.