Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

OBJECTIVE 2 Divide a polynomial by a polynomial of two or more terms.


This process is similar to that for dividing whole numbers.


Dividing a Polynomial by a Polynomial

Divide.


Make sure each polynomial is written in descending powers of the variables.


Divide the first term of the dividend by the first term of the divisor


Here


Result of

Multiply and and write the result below


Now subtract by mentally changing the signs on and adding.


Subtract. The difference is 5m.

Bring down and continue by dividing 5mby m.


Bring down -10.

Subtract. The difference is 0.

CHECK Multiply (the divisor) and (the quotient). The result is


2 m^2 +m- 10 (the dividend). ✓


m- 2 2 m+ 5


0


5 m- 10 51 m- 22 = 5 m- 10


5 m- 10


2 m^2 - 4 m


m- 2  2 m^2 + m- 10


5 m

2 m+ (^5) m = 5


- 10


5 m


2 m^2 - 4 m


m- 2  2 m^2 + m- 10


2 m


2 m^2 - 4 m


2 m^2 - 4 m 2 m 1 m- 22 = 2 m^2 - 4 m


m- 2  2 m^2 + m- 10


2 m


m- 2 2 m, 2 m^2 + m-10.


m- 2  2 m^2 +m- 10


2 m^2

2 m m


2 m^2

m-2. m = 2 m.


2 m^2 + m- 10


m- 2  2 m^2 +m- 10


2 m^2 + m- 10


m- 2


EXAMPLE 2


SECTION 5.5 Dividing Polynomials 303


NOW TRY

To subtract,
add the opposite.

Write as if dividing
whole numbers.

Dividing a Polynomial with a Missing Term

Divide by


Make sure that is in descending powers of the variable. Add a term


with 0 coefficient as a placeholder for the missing -term.


Missing term

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


x^2


3 x^3 - 2 x+ 5


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


EXAMPLE 3


NOW TRY
EXERCISE 2
Divide.


3 x^2 - 4 x- 15
x- 3

NOW TRY ANSWER



  1. 3 x+ 5

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