# Class 10: Remainder and Factor Theorems – ICSE Board Problems

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

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]

When , Remainder

… … … … … i)

When , Remainder

… … … … … ii)

Solving i) and ii), we get

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

When , Remainder

Therefore

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

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]

When

Remainder1

Remainder2

Given Remainder1 = Remainder 2

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

Let

Remainder

Hence is a factor of

•
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•
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•
•

Hence

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