Intermediate Algebra (11th edition)

Adding Polynomials

Add

Commutative and

= 3 a associative properties

(^5) - 8 a (^5) - 9 a (^3) + 8 a (^3) + 4 a (^2) + 2

13 a^5 - 9 a^3 + 4 a^22 + 1 - 8 a^5 + 8 a^3 + 22

13 a^5 - 9 a^3 + 4 a^22 + 1 - 8 a^5 + 8 a^3 + 22.

EXAMPLE 4

SECTION 5.2 Adding and Subtracting Polynomials 281

In Section 1.2,we defined subtraction of real numbers as follows.

That is, we add the first number and the negative (or opposite) of the second. We de-

fine the negative of a polynomialas that polynomial with the sign of every coeffi-

cient changed.

aba 1 b 2

Subtracting Polynomials

To subtract two polynomials, add the first polynomial (minuend) and the nega-

tive (or opposite) of the secondpolynomial (subtrahend).

Subtracting Polynomials

Subtract

Change every sign in the second polynomial (subtrahend) and add.

Definition of subtraction

Rearrange terms.

Combine like terms.

CHECK ✓

Answer Subtrahend Minuend

Alternatively, we can subtract these two polynomials vertically.

- 5 m^2 + 7 m- 8

- 6 m^2 - 8 m+ 5

1 - m^2 - 15 m+ 132 + 1 - 5 m^2 + 7 m- 82 =- 6 m^2 - 8 m+ 5

=-m^2 - 15 m+ 13

=- 6 m^2 + 5 m^2 - 8 m- 7 m+ 5 + 8

=- 6 m^2 - 8 m+ 5 + 5 m^2 - 7 m+ 8

1 - 6 m^2 - 8 m+ 52 - 1 - 5 m^2 + 7 m- 82

1 - 6 m^2 - 8 m+ 52 - 1 - 5 m^2 + 7 m- 82.

EXAMPLE 5

Write the subtrahend below

the minuend, lining up like

terms in columns.

Change all the signs in the subtrahend and add.

Change all signs.

- m^2 - 15 m+ 13 Add in columns. NOW TRY

+ 5 m^2 - 7 m+ 8

- 6 m^2 - 8 m+ 5

NOW TRY
EXERCISE 4
Add.

1 x^3 - 3 x^2 - 52

17 x^2 - 9 x+ 42 +

NOW TRY
EXERCISE 5
Subtract.

18 y^2 - 2 y+ 102

12 y^2 - 7 y- 42 -

NOW TRY ANSWERS
4.

5. 
   
   
   
   • 6 y^2 - 5 y- 14
   
   
   
   

x^3 + 4 x^2 - 9 x- 1

Combine like terms.

Alternatively, we can add these two polynomials vertically.

Place like terms in columns.

- 5 a^5 - a^3 + 4 a^2 + 2 NOW TRY

- 8 a^5 + 8 a^3 + 2

3 a^5 - 9 a^3 + 4 a^2

= - 5 a^5 - a^3 + 4 a^2 + 2

The answer

is the same.