Question 1: If has as a factor and leaves a remainder of when divided by , find the value of . ** [2005]**

Answer:

When , Remainder

… … … … … i)

When , Remainder

… … … … … ii)

Solving i) and ii)

Question 2: If is a factor of the expression and when the expression is divided by , it leaves a remainder . Find the value of . **[2013]**

Answer:

When , Remainder

… … … … … i)

When , Remainder

… … … … … ii)

Solving i) and ii), we get

Question 3: Find the value of , if is a factor of . ** [2003]**

Answer:

When , Remainder

Therefore

Question 4: Using remainder theorem, factorize completely. ** [2014]**

Answer:

For ,

Remainder:

Hence is a factor of

Hence

Question 5: When divided by the polynomials and leave the same remainder. Find the value of . ** [2010]**

Answer:

When

Remainder1

Remainder2

Given Remainder1 = Remainder 2

Question 6: Use the remainder theorem to factorize the following expression: . ** [2010]**

Answer:

Let

Remainder

Hence is a factor of

Hence

Question 7: Find the value of if is a factor of . Hence determine whether is also a factor. **[2011]**

Answer:

Let .

Since given that is a factor

Substituting the value of in the above function we get:

For to be a factor

Substituting the value of in the above function we get:

Hence ) is a factor of