Beginning Algebra, 11th Edition

CHECK Multiply the divisor, by the quotient, The product must be

the original dividend,

✓

Divisor Quotient

Dividend NOW TRY

Dividing a Polynomial by a Polynomial

Divide.

The first polynomial must be written in descending powers as

Then divide by

- 6 Remainder

4 x- 2

4 x- 8

- 2 x^2 + x

- 2 x^2 + 5 x

4 x^3 - 2 x^2

2 x- 1  4 x^3 - 4 x^2 + 5 x- 8

2 x^2 - x+ 2

2 x- 1.

4 x^3 - 4 x^2 + 5 x- 8.

5 x+ 4 x^3 - 8 - 4 x^2

2 x- 1

EXAMPLE 6

= 3 x^2 - 5 x- 28

1 x- 4213 x+ 72 = 3 x^2 + 7 x- 12 x- 28

3 x^2 - 5 x-28.

x-4, 3 x+7.

Each time you

subtract, add

the opposite.

Write in

descending

powers.

Step 1 divided by.

Step 2 Subtract. Bring down the next term.

Step 3 divided by.

Step 4 Subtract. Bring down the next term.

Step 5 4 xdivided by is.

Step 6 Subtract. The remainder is. Write the remainder as the numerator of a

fraction that has as its denominator. Because of the nonzero

remainder, the answer is not a polynomial.

4 x^3 - 4 x^2 + 5 x- 8

2 x- 1

= 2 x^2 - x+ 2 +

- 6

2 x- 1

2 x- 1

- 6

2 x 2 212 x- 12 = 4 x- 2

- 2 x^22 x is -x -x 12 x- 12 =- 2 x^2 +x

4 x^32 x is 2 x^22 x^212 x- 12 = 4 x^3 - 2 x^2

Dividend

Divisor

Quotient

polynomial Fractional part

of quotient

Remainder

Divisor

344 CHAPTER 5 Exponents and Polynomials

Remember to add.

Don’t forget the sign.+

remainder

divisor

Dividing a Polynomial by a Polynomial

Divide.

Step 1 divided by xis 3x.

3 x 1 x- 42 = 3 x^2 - 12 x

3 x^2

3 x^2 - 5 x- 28

x- 4

EXAMPLE 5

Step 2 Subtract from

Bring down

Step 3 7 xdivided by xis 7.

Step 4 Subtract 7 x- 28 from 7 x- 28.The remainder is 0.

71 x- 42 = 7 x- 28

3 x^2 - 5 x. -28.

3 x^2 - 12 x

NOW TRY
EXERCISE 5
Divide.

4 x^2 +x- 18

x- 2

NOW TRY ANSWER

5. 4 x+ 9

Quotient

Dividend

Divisor

0

7 x- 28

7 x- 28

3 x^2 - 12 x

x- 4  3 x^2 - 5 x- 28

3 x+ 7

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