Long Division: Another Example (4.1.2)

Question 1

• When you see a rational expression composed of polynomials, you can divide the numerator by the denominator.

Answer 1

• When you see a rational expression composed of polynomials, you can divide the numerator by the denominator.

Question 2

• Division with polynomials is very similar to division with real numbers. Use the same steps you used in elementary school.

Answer 2

• Division with polynomials is very similar to division with real numbers. Use the same steps you used in elementary school.

Question 3

• Be careful to match like terms when you are adding and subtracting. The area for focus is to be sure that all the exponents match.

Answer 3

• Be careful to match like terms when you are adding and subtracting. The area for focus is to be sure that all the exponents match.

Question 4

In this example, (x + 4) can divide into the numerator,
(x
4
– 4x
2
+ 7x – 15).
Once the problem is set up, ask yourself “What can I multiply
with x to have an answer of x
4
?”
x
3
, of course.
x
3
is the first term of your answer. Multiply it with both x
and 4, and write the answers under their matching terms.
Next, subtract your products from the terms in the polynomial
being divided.
Note: Arrange the terms in descending order with any
missing exponents written in with coefficients of 0. This
greatly helps you line up your terms and subtract properly.
Now, repeat the process using the terms derived from your
first cycle of multiplying and subtracting.
Repeat this until all terms have been used.
Note any remainder. Sometimes remainders are written in a
fraction with the dividing number as the denominator.
All of these steps are the same ones used for dividing with real numbers.

Answer 4

In this example, (x + 4) can divide into the numerator,
(x
4
– 4x
2
+ 7x – 15).
Once the problem is set up, ask yourself “What can I multiply
with x to have an answer of x
4
?”
x
3
, of course.
x
3
is the first term of your answer. Multiply it with both x
and 4, and write the answers under their matching terms.
Next, subtract your products from the terms in the polynomial
being divided.
Note: Arrange the terms in descending order with any
missing exponents written in with coefficients of 0. This
greatly helps you line up your terms and subtract properly.
Now, repeat the process using the terms derived from your
first cycle of multiplying and subtracting.
Repeat this until all terms have been used.
Note any remainder. Sometimes remainders are written in a
fraction with the dividing number as the denominator.
All of these steps are the same ones used for dividing with real numbers.