Basic Mathematics for College Students

The binomials in Example 3 can be added by writing the polynomials so that like

terms are in columns.

Add the like terms, one column at a time.

2 x 3

 7 x 1

9 x 2

A-10 Appendix II Polynomials

Solution

Write a sign between the binomials.

Use the associative and commutative properties to

group like terms together.

 9 x 2 Combine like terms.

 12 x 7 x 2  13  12

12 x 32  17 x 12

EXAMPLE (^4) Add: (5x^2  2 x4) (3x^2 5)
StrategyWe will combine the like terms of the trinomial and binomial.
WHYTo add polynomials, we combine like terms.
Solution
Use the associative and commutative
properties to group like terms together.
 8 x^2  2 x 1 Combine like terms.
 15 x^2  3 x^22  1  2 x 2  14  52
15 x^2  2 x 42  13 x^2  52
Self Check 4
Add:
(2b^2  4 b) (b^2  3 b1)
Now TryProblem 33
The polynomials in Example 4 can be added by writing the polynomials so that
like terms are in columns.
Add the like terms, one column at a time.
5 x^2  2 x 4
 3 x^2  5
8 x^2  2 x 1
EXAMPLE (^5) Add: (3.7x (^2)  4 x2) (7.4x (^2)  5 x3)
StrategyWe will combine the like terms of the two trinomials.
WHYTo add polynomials, we combine like terms.
Solution
Use the associative and
commutative properties to
group like terms together.
 11.1x^2 x 1 Combine like terms.
 1 3.7x^2 7.4x^22  14 x 5 x 2  1  2  32
1 3.7x^2  4 x 22  1 7.4x^2  5 x 32
Self Check 5
Add:
(s^2 1.2s5)(3s^2 2.5s4)
Now TryProblem 37
The trinomials in Example 5 can be added by writing them so that like terms are
in columns.
Add the like terms, one column at a time.
3.7x^2  4 x 2
 7.4x^2  5 x 3
11.1x^2  x 1