Division of Polynomial by Binomial

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Division of Polynomial by Binomial using Long Division

For dividing a polynomial by a binomial, we may proceed according to the following steps :

(1) Arrange the terms of the dividend and the divisor in descending order of their exponents.
(2) Divide the 1st term of the dividend by the 1st term of the divisor to obtain the 1st term of the quotient.
(3) Multiply the divisor by the 1st term of the quotient and subtract the result from the dividend to obtain the remainder.
(4) Consider the remainder as dividend and repeat the step(2) to obtain the 2nd term of the quotient.
(5) 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

(a2 + 7a + 12) ÷ (a + 4)
Step 1: We look at the first term of (a2 + 7a + 12 )and the first term of (a + 4)
Divide as follows : a2/a
We write 'a' at top of our long division and multiply
(a)(a + 4)= a2 + 4a to give the second row of our solution
Step 2 : Subtracting the second row from the first gives :
Be careful with
+ 7a - (+ 4a ) = +7a - 4a = 3a

Step 3: Bring down the +12 from the 1st row :
Step 4: As the remainder is 3a + 12, so multiply (a +4) by 3 and write +3 at the top.Write the multiplication of 3 and (a + 4) below the remainder.
Step 5: Subtract : (3a + 12) and ( 3a + 12)

So (a2 + 7a + 12)/ (a + 4) = a + 3
You can check your answer by multiplying (a + 3) by (a +4) you will get (a2 + 7a + 12)


Division of Algebraic Expressions

Division of Polynomial by Monomial
Division of Polynomial by Binomial

Algebraic Expression Page

Home Page

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.