Teaching Notes 5.3: Adding Polynomials
Adding polynomials is an important algebraic skill. A common error students make when adding
polynomials is to add unlike terms.- Provide this example: A teacher asked two students to help collect worksheets and calcu-
lators at the end of the class. Two students volunteer to help. One collects 15 worksheets
and 10 calculators and the other student collects 8 worksheets and 5 calculators. Ifwrepre-
sents the number of worksheets andcrepresents the number of calculators, (15w+ 10 c)+
(8w+ 5 c) shows the number of items collected. Note that the parentheses enclose the items
collected by each student. Explain that to find the sum (or total number of worksheets and
calculators), your students should add the number of worksheets together and then add the
number of calculators: 15w+ 8 w+ 10 c+ 5 c= 23 w+ 15 cor 23 worksheets and 15 calcula-
tors. Emphasize that the sum is found by adding similar terms: the coefficients of the variable
wwere added and the coefficients of the variablecwere added. - Explain that to add polynomials the coefficients of all of the similar terms must be added just
as students would add integers. Also note that the numbers that have no variables are called
‘‘constants’’ and can be added with other constants, following the rules for adding integers.
Depending on the abilities of your students, you may find it necessary to review the steps for
adding integers. - Review the information and examples on the worksheet with your students. Make sure your
students understand what constitutes similar terms.
EXTRA HELP:
Only the coefficients of similar terms can be added. If two terms are not similar, they cannot be
added.ANSWER KEY:
(1) 7 x+ 5 (2) 2 x^2 +x (3) 6 a+ 4 b+ 1 (4) 4 x^2 +x+ 10 (5)− 7 (6) 3 x^2 +xy+ 2 (7) 9 a^2 − 5
(8) 2 y− 5 xy− 11 x (9) 4 (10) 4 x^2 + 7 x− 21
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(Challenge)The sum of polynomials will never contain any similar terms because similar
terms must be combined when added.
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