Division of Polynomial by Binomial

Division of Polynomial by Monomial

Division of Polynomial by Binomial

Before you understand how to divide polynomial, you are advised to read: What is Polynomial ? What is Monomial & Binomial ? Lets understand how to divide a polynomial by a binomial, with the help of following example: Example 1: Divide 4a2 + 2a - 3 by a + 2 Solution: As per the given question: Polynomial = Dividend= 4a2 + 2a - 3 Binomial = Divisor = a + 2 Step of division are as follows: Step 1: Write the dividend and division as shown below: Step 2: Divide first term of dividend by first term of divisor i.e. 4a2 ÷ a = 4a. Now, 4a will be first term of quotient (as shown below) Step 3: Multiply the first term of quotient (calculated in step 2) with divisor i.e. 4a(a + 2) = 4a2 + 8a and place it below the dividend, as shown below: Step 4: Subtract, product of divisor and first term of quotient, from the dividend. (as shown below) Step 5: Now take next term of dividend i.e.-3 and place it next to the term i.e. -6a; which we got after subtraction in step 4 (as shown below) Step 6: Thus we got (-6a - 3) as new dividend (as shown below). (From now onwards, procedure from step 2 will be repeated) Step 7: (Repeat step 2) Divide first term of new dividend by first term of divisor i.e. -6a ÷ a = -6. Now -6 will be second term of quotient (shown below) Step 8: (Repeat step 3) Multiply the second term of quotient (calculated in step 7) with divisor i.e. -6(a + 2) = -6a - 12 and place it below the dividend, as shown below: Step 9: (Repeat Step 4) Subtract, product of divisor and second term of quotient, from the new dividend. And after the subtraction we get 9 as remainder (as shown below). Hence, when (4a2 + 2a - 3) is divided by (a + 2), we get (4a - 6) as quotient and 9 as remainder Or we can write it as: (4a2 + 2a - 3) = (a + 2) (4a - 6) + 9