Division of Polynomial by Binomial
Division of Polynomial by Binomial using Long DivisionFor 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
(a^{2} + 7a + 12) ÷ (a + 4)
Step 1: We look at the first term of (a^{2} + 7a + 12 )and the first term of (a + 4) Divide as follows : a^{2}/a We write 'a' at top of our long division and multiply (a)(a + 4)= a^{2} + 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 (a^{2} + 7a + 12)/ (a + 4) = a + 3 You can check your answer by multiplying (a + 3) by (a +4) you will get (a^{2} + 7a + 12) |
Division of Algebraic Expressions
• Division of Polynomial by Monomial
• Division of Polynomial by Binomial
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