SECTION 5.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials^323
The polynomials in Example 5also can be added horizontally.
Adding Polynomials Horizontally(a)Add and
Combine like terms.
Same answer as found
in Example 5(a)(b)Add and
Commutative property
Combine like terms.
NOW TRYIn Section 1.5,we defined the difference as (We find the dif-
ference by adding xand the opposite of y.) For example,
and
A similar method is used to subtract polynomials.
7 - 2 = 7 + 1 - 22 = 5 - 8 - 1 - 22 =- 8 + 2 =-6.
x-y
x-y x+ 1 - y 2.
= x^3 + 2 x^2 + x+ 3
= x^3 + 2 x^2 - 4 x+ 5 x+ 3
12 x^2 - 4 x+ 32 + 1 x^3 + 5 x 2
2 x^2 - 4 x+ 3 x^3 + 5 x.
16 x^3 - 4 x^2 + 32 + 1 - 2 x^3 + 7 x^2 - 52 = 4 x^3 + 3 x^2 - 2
6 x^3 - 4 x^2 + 3 - 2 x^3 + 7 x^2 - 5.
EXAMPLE 6
Subtracting Polynomials Horizontally(a)Perform the subtraction
Definition of subtractionDistributive property
Combine like terms.(b)Subtract from
AnswerCHECK To check a subtraction problem, use the fact that
if then
Here, add and
= 11 x^3 + 2 x^2 - 8 ✓ NOW TRY
16 x^3 - 4 x^2 + 22 + 15 x^3 + 6 x^2 - 102
6 x^3 - 4 x^2 + 2 5 x^3 + 6 x^2 - 10.
a- b= c, a=b+c.
= 5 x^3 + 6 x^2 - 10
= 111 x^3 + 2 x^2 - 82 + 1 - 6 x^3 + 4 x^2 - 22
111 x^3 + 2 x^2 - 82 - 16 x^3 - 4 x^2 + 22
6 x^3 - 4 x^2 + 2 11 x^3 + 2 x^2 - 8.
= 2 x+ 6
= 15 x- 22 + 1 - 3 x+ 82
= 15 x- 22 + 3 - 113 x- 824 - a=- 1 a
= 15 x- 22 + 3 - 13 x- 824
15 x- 22 - 13 x- 82
15 x- 22 - 13 x- 82.
EXAMPLE 7
Be careful to write
the problem in the
correct order.NOW TRY
EXERCISE 6
Add and
x^4 - 3 x^2 + 5 xhorizontally.
10 x^4 - 3 x^2 - xNOW TRY
EXERCISE 7
Subtract from
4 t^4 - t^2 +7.
5 t^4 - 3 t^2 + 1NOW TRY ANSWERS
6.
7.-t^4 + 2 t^2 + 6
11 x^4 - 6 x^2 + 4 xSubtracting Polynomials
To subtract two polynomials, change all the signs in the second polynomial
and add the result to the first polynomial.