Teaching Notes 5.11: Dividing Polynomials
The steps for dividing one polynomial by another are similar to the steps for dividing whole
numbers. Just as with long division, students often become confused by the process or make
errors in computation.- Explain that polynomials can be divided following the same process as dividing whole num-
bers: divide, multiply, subtract, and bring down the next term. To demonstrate these steps,
offer an example by using long division to divide 328 by 15. The quotient is 21, r 13, or 21
13
15
.
- Explain that before dividing polynomials, each polynomial must be written so that the expo-
nents are in descending order. Provide this example: (x− 1 + 2 x^2 )÷(3+x)mustberewrit-
ten as (2x^2 +x−1)÷(x+3). If an exponent is ‘‘missing,’’ the term must be rewritten with
0 as the coefficient. For example, (x^3 + 2 x−1)÷(x+4) is written in descending order but
there is nox^2 term in the first polynomial. This polynomial must be rewritten asx^3 + 0 x^2 +
2 x−1. - Review the information and example on the worksheet with your students. Discuss each
step for division. Caution your students to be especially careful when subtracting. Depend-
ing on the abilities of your students, you might find it helpful to review 5.4: ‘‘Subtracting
Polynomials.’’
EXTRA HELP:
You may check your answer by multiplying the quotient by the divisor and adding the numerator
of the fraction that remains.ANSWER KEY:
(1)x− 1 +5
x+ 4
(2) 2 x− 4 +9
x+ 1
(3) 3 x− 10 +10
x+ 2
(4)x+ 2 +9
x− 4(5) 2 x− 1 +1
2 x− 1
(6)x− 2 +3
x+ 2
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(Challenge)Tyrell did not write the terms in descending order of the exponents. He should
have included anxterm. The correct way of rewriting the polynomial isx^3 +x^2 + 0 x+1.
------------------------------------------------------------------------------------------196 THE ALGEBRA TEACHER’S GUIDE