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,
Example: Divide
Solution:
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 |
Divide by 2y - 1, then find the quotient | |||
Right Option : C | |||
View Explanation |
The process of division of a polynomial by another polynomial does not stop until ____________________ | |||
Right Option : C | |||
View Explanation |
I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.