Beginning Algebra, 11th Edition

OBJECTIVE 4 Evaluate polynomials. A polynomial usually represents differ-

ent numbers for different values of the variable.

Evaluating a Polynomial

Find the value of for (a) and (b)

(a)First, substitute for x.

Let

Apply the exponents.

Multiply.

Add and subtract.

(b)

Let

Apply the exponents.

Multiply.

= 362 Add and subtract. NOW TRY

= 243 + 135 - 12 - 4

= 31812 + 51272 - 12 - 4

= 31324 + 51323 - 4132 - 4 x=3.

3 x^4 + 5 x^3 - 4 x- 4

= 12

= 48 - 40 + 8 - 4

= 31162 + 51 - 82 - 41 - 22 - 4

= 31 - 224 + 51 - 223 - 41 - 22 - 4 x=-2.

3 x^4 + 5 x^3 - 4 x- 4

- 2

3 x^4 + 5 x^3 - 4 x- 4 x=- 2 x= 3.

EXAMPLE 4

Use parentheses

to avoid errors.

CAUTION Use parentheses around the numbers that are substituted for the vari-

able, as in Example 4.Be particularly careful when substituting a negative number

for a variable that is raised to a power, or a sign error may result.

OBJECTIVE 5 Add and subtract polynomials.

NOW TRY
EXERCISE 4
Find the value for.

4 t^3 - t^2 - t

t=- 3

NOW TRY
EXERCISE 5
Add and
y^3 - y- 7 vertically.

4 y^3 - 2 y^2 +y- 1

NOW TRY ANSWERS
4.

5. 5 y^3 - 2 y^2 - 8
   
   
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Adding Polynomials Vertically

(a)Add and

Now add, column by column.

Add the three sums together.

Final sum

(b)Add and

Write like terms in columns and add column by column.

x^3 + 2 x^2 + x+ 3 NOW TRY

x^3 + 5 x

2 x^2 - 4 x+ 3

2 x^2 - 4 x+ 3 x^3 + 5 x.

4 x^3 + 3 x^2 + 1 - 22 = 4 x^3 + 3 x^2 - 2

4 x^33 x^2 - 2

- 2 x^37 x^2 - 5

6 x^3 - 4 x^23

- 2 x^3 + 7 x^2 - 5

6 x^3 - 4 x^2 + 3

6 x^3 - 4 x^2 + 3 - 2 x^3 + 7 x^2 - 5.

EXAMPLE 5

322 CHAPTER 5 Exponents and Polynomials

Combine the

coefficients only.

Do notadd the

exponents.

Leave spaces for

missing terms.

Adding Polynomials

To add two polynomials, add like terms.

Write like terms in columns.

Replace xwith 3.

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