Intermediate Algebra (11th edition)

Start with

Subtract by mentally changing the signs on and adding.

Subtract.

Bring down the next term.

Bring down

In the next step,

Subtract. Bring down 5.

Finally,

Remainder

Write the remainder, 80, as the numerator of the fraction.

3 x^3 - 2 x+ 5

x- 3

= 3 x^2 + 9 x+ 25 +

80

x- 3

80

x- 3

80

25 x- 75 251 x- 32

25 x+ 5

9 x^2 - 27 x

9 x^2 - 2 x

3 x^3 - 9 x^2

x- 3  3 x^3 + 0 x^2 - 2 x+ 5

25 x

3 x x = 25

(^2) + 9 x+ 25
25 x

x = 25.

25 x+ 5

9 x^2 - 27 x 9 x 1 x- 32

9 x^2 - 2 x

3 x^3 - 9 x^2

x- 3  3 x^3 + 0 x^2 - 2 x+ 5

9 x^2

3 x x = 9 x

(^2) + 9 x
9 x^2

x =^9 x.

9 x^2 - 2 x - 2 x.

3 x^3 - 9 x^2

x- 3  3 x^3 + 0 x^2 - 2 x+ 5

3 x^2

9 x^2

3 x^3 - 9 x^2

x- 3  3 x^3 + 0 x^2 - 2 x+ 5

3 x^2

3 x^3 - 9 x^2

3 x^3 - 9 x^23 x^21 x- 32

x- 3  3 x^3 + 0 x^2 - 2 x+ 5

3 x^3

x =^3 x

3 x^22

3 x^3

x =^3 x

(^2).

304 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

NOW TRY
EXERCISE 3
Divide

2 x^3 - 12 x-10 by x-4.

Be sure to add.

Don’t forget the+sign.

remainder

divisor

CHECK Multiply (the divisor) and (the quotient), and then

add 80 (the remainder). The result is 3 x^3 - 2 x+5. ✓

x- 3 3 x^2 + 9 x+ 25

NOW TRY

CAUTION Remember to include as part of the answer. Don’t forget to

insert a plus sign between the polynomial quotient and this fraction.

remainder
NOW TRY ANSWER divisor

3. 2 x^2 + 8 x+ 20 +x^70 - 4