Dividing by a Binomial - Watch video (Amsco Integrated Algebra I)

Amsco Integrated Algebra I: Dividing by a Binomial

This is a free lesson from our course in Amsco's Integrated Algebra


	In this lesson you’ll learn how to divide a polynomial by a binomial. Let us begin with simpler illustration to divide 736 by 32, where we use repeated subtraction of multiples of 32 to determine how many times 32 are contained in 736. To divide a polynomial by a binomial, use a similar procedure i.e. subtract multiples of the divisor from the dividend until the remainder is zero or of degree less than the degree of the divisor. You’ll just see the steps below in detail: Step1. First arrange the terms of the dividend in descending order. Step2. Divide the first term of the dividend by the first term of the divisor, to obtain the first term of the quotient. (More text below video...)

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(Continued from above) Step3. Multiply the whole divisor by the first term of the quotient and write each term of the product under the like term of the dividend
Step4. Subtract and bring down the next term of the dividend to obtain a new dividend
Step5. Divide the first term of the new dividend by the first term of the divisor to obtain the next term of the quotient
Step6. Repeat steps (3) and (4) above, multiplying the whole divisor by the new term of the quotient. Subtract this product from the new dividend.
Here the remainder is zero and the division is complete. The division can be checked by multiplying the quotient by the divisor to obtain the dividend.
For Example: Divide 3a² – 8a + 4 by a – 2.
It can be solved using the above procedure steps and see the solution below-
First arrange the terms of the dividend in descending order: 3a² – 8a + 4, solve it and then check.

Given: Divide 3a² – 8a + 4 by a – 2 and check. Follow the steps below to solve,

   a – 2
   ____________
3a – 2 ) 3a² – 8a + 4
    3a² – 2a
– +
          _______________
   – 6a + 4
   – 6a + 4
+    -
   _______________
      0
The final answer is: a – 2

Check
(a – 2)(3a – 2)
= a(3a – 2) – 2(3a – 2)
= 3a² – 2a – 6a + 4
= 3a² – 8a + 4

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