Question 1: In each of the following cases, find the remainder when

Answer:

i) Required Remainder = Value of given polynomial

ii) Required Remainder = Value of given polynomial

iii) Required Remainder = Value of given polynomial

Question 2: Show that

Answer:

, then the remainder should be

, then the remainder should be

Question 3: Find which of the following is a factor of

Answer:

, then the remainder should be

, then the remainder should be

is NOT a factor of

, then the remainder should be

Question 4: Find the value of if

Answer:

Question 5: Find the value of , when

Answer:

is a factor

… … … … … i)

Similarly, is a factor

… … … … … ii)

Solving i) and ii) we get

is a factor

… … … … … i)

is a factor

… … … … … ii)

Solving i) and

Question 6: , the remainder is . Find .

Answer:

,

Question 7: Find the value of , if the division of by leaves a remainder of .

Answer:

,

Question 8: has as a factor and leaves a remainder of when divided by , find the value of . [2005]

Answer:

,

… … … … … i)

,

… … … … … ii)

Solving i) and

Answer:

… … … … … i)

,

… … … … … ii)

Solving i) and

Question 10: What number should be added to , so that when it is divided by , the remainder is .

Answer:

be added to , so that when it is divided by , the remainder is

, Remainder is

Question 11: What number should be subtracted to , so that when it is divided by , the remainder is .

Answer:

be subtracted to , so that when it is divided by , the remainder is

, Remainder is

Question 12: The polynomials and leave the same remainder when divided by . Find the value of .

Answer:

:

:

Therefore

Question 13: is a factor of the expression and when the expression is divided by , it leaves a . Find the value of . [2013]

Answer:

,

… … … … … i)

,

… … … … … ii)

Solving i) and ii), we get