Division of Polynomial by another Polynomial Long Division
Division of Polynomial by another Polynomial Long Division
Division of a polynomial by a binomial by using long division
For dividing a polynomial by a binomial, we may follow the following steps:
Step I Arrange the terms of the dividend and divisor in descending order of their degrees.
Step II Divide the first term of the dividend by the first term of the divisor to obtain the first term of the
quotient.
Step III Multiply the divisor by the first term of the quotient and subtract the result from the dividend to
obtain the remainder.
Step IV Consider the remainder (if any) as dividend and repeat step II to obtain the second term of
quotient.
Step V Repeat the above process till we obtain a remainder which is either zero or a polynomial of
degree less than that of the divisor.
Example 1 Divide
Solution We go through the following steps to perform the division:
Step I We write the terms of the dividend as well as of divisor in descending order of their
degrees. Thus, we write
Step II We divide the first term of the dividend by the first term
of the divisor and obtain
as the first term of the quotient.
Step III We multiply the divisor by the first term
we get
of the quotient
and subtract the result from the dividend
We obtain as the remainder.
Step IV We take as the new dividend and repeat step II to obtain the second
term of the quotient.
Step V We multiply the divisor by the second term
of the quotient and subtract the
result from the new dividend. We obtain
as the remainder.
Step VI Now we treat as the new dividend and divide its first term
by the first
term of the divisor to obtain
as the third term of the quotient.
Step VII We multiply the divisor and the third term
of the quotiemt and subtract the
result from the new dividend. We obtain
as the remainder.
Thus, we can say that
or,
Divide | |||
| Right Option : C | |||
| View Explanation | |||
The coefficient of the first term of the quotient when the polynomial p(x)= | |||
| Right Option : B | |||
| View Explanation | |||
Find the remainder: | |||
| Right Option : B | |||
| View Explanation | |||
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