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Find the remainder when is divided by (i) x+1 (ii)
(iii) x (iv)
(v) x+2x
(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
Find the remainder when is divided by x – a.
By long division,
Therefore, when x3 − ax2 + 6x − a is divided by x − a, the remainder obtained is 5a.
Check whether 7 + 3x is a factor of
Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3x will 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.
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