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,
If the degree of the dividend is 5 and the degree of the divisor is 3, then the degree of the quotient will be ________________- | |||
Right Option : D | |||
View Explanation |
If is divided by , then the possible degrees of quotient and remainder are ___________________ | |||
Right Option : A | |||
View Explanation |
If is divided by g(x) and quotient is , then the possible degree of remainder is _____________________ | |||
Right Option : C | |||
View Explanation |
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