Page 729 - Basic College Mathematics with Early Integers

A PPEND I X B .1 I ADDING AND SUBTRACTING POLYNOMIALS 705

Below are examples of monomials, binomials, and trinomials. Each of these
examples is also a polynomial.

Polynomials
Monomials Binomials Trinomials More Than Three Terms
2
2
3
z x + 2 x - 2x + 1 5x - 6x + 2x - 10
1 1
4 r - y + 3y - 1.7 t - t + t - t + 1
7
5
3
5
2
3 2
3
4
2
8
2
3
0.2x 2 -1.2y + 0.7y -a + 2a - 5a z - z + 3z - 2z
c c c
1 term 2 terms 3 terms
To add polynomials, we use the commutative and associative properties to
rearrange and group like terms.Then, we combine like terms.
Adding Polynomials
To add polynomials, combine like terms.
Example 1 Add: 13x - 12 + 1-6x + 22 PRACTICE 1
Add: 12y + 72 + 19y - 142
Solution:

13x - 12 + 1-6x + 22 = 13x - 6x2 + 1-1 + 22 Group like terms.
= 1-3x2 + 112 Combine like terms.
=-3x + 1
Work Practice 1

Example 2 Add: 19y - 6y2 + 17y + 10y + 22 PRACTICE 2
2
2
Add:
Solution: 15x + 4x - 32 + 1x - 6x2
2
2
2
2
2
2
19y - 6y2 + 17y + 10y + 22 = 9y + 7y - 6y + 10y + 2 Group
like terms.
2
= 16y + 4y + 2
Work Practice 2
Example 3 Find the sum of 1-y + 2y + 1.72 and 112y - 6y - 3.62. PRACTICE 3
2
2
Find the sum of
Solution: Recall that “sum” means addition. 17z - 4.2z + 112 and
2
2 2 2
1-y + 2y + 1.72 + 112y - 6y - 3.62 1-9z - 1.9z + 42.
2
2
=-y + 12y + 2y - 6y + 1.7 - 3.6 Group like terms.
e d d
2
= 11y - 4y - 1.9 Combine like terms.
Work Practice 3
Polynomials can also be added vertically. To do this, line up like terms under-
neath one another. Let’s vertically add the polynomials in Example 3. Answers
2
1. 11y - 7 2. 6x - 2x - 3
2
3. -2z - 6.1z + 15