Polynomial Long Division

By yellowsub68 | Updated: Nov. 1, 2024, 5:35 a.m.

Slideshow Video

SHARE THE AWESOMENESS

This video walks through long division of polynomials. It begins with a quick problem using traditional long division, then a step-by-step guide on polynomial long division, including writing the remainder as a fraction. Afterwards, it completes two more problems, inputting a missing term in either the divisor or dividend.

Education

create your own animated videos for free

_abc cc

* Powtoon is not liable for any 3rd party content used. It is the responsibility of each user to comply with 3rd party copyright laws.

Embed code

Select a size, the embed code changes based on your selection.

_abc Powtoon Transcript

A Serano Production
Polynomial
Polynomial
Long
Long
Division
Division
Before we try division of polynomials,
let's review traditional long division.
Divide              14   4,304
)
_______
How many times does 14 go into 4?
14 doesn't go into 4, so move on.
How many times does 14 go into 43?
14 divides into 43 THREE times, because
14 x 3 = 42.
Divide              14   4,304
)
_______
3
You need to write the 3 over the second number to match it up with 43, not just with the 4.
________
___
- 4 2
___
1
Bring down the next number.
0
How many times does 14 go into 10?
How many times does 14 go into 43?
Divide              14   4,304
)
_______
3
- 4 2
___
1
0
14 doesn't go into 10, so write a ZERO on top and bring down the next number.
o
4
How many times does 14 go into 104?
14 divides into 104 SEVEN times, because
14 x 7 = 98.
7
Bring down the next number.
How many times does 14 go into 10?
Divide              14   4,304
)
_______
3
- 4 2
___
1
0
o
4
7
- 9 8
____
6
Write the remainder as a fraction.
6
__
14
Reduce the fraction, if possible.
=  307
3
_
7
How many times does 14 go into 104?
Now let's try Long Division with Polynomials
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
Compare the first term in the divisor and the dividend.
What would you multiply to x
to get x  ?
3
x
2
x
2
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
Notice we wrote x  over the second term.  
x
2
Because there are two terms in the divisor, 
we need to start our answer over the second term.
Multiply x   times each term in the divisor, then write the products under the first two terms.
2
x
3
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
Multiply x   times each term in the divisor, then write the products under the first two terms.
2
x
3
- 2x
2
When you came to this step in traditional long division, what did you do?
We subtracted
HINT!
Just change the signs
-
+
_______
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
x
3
- 2x
2
-
+
_______
/
6x
2
When you came to this step in traditional long division, what did you do?
We brought down the next number
- 5x
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
x
3
- 2x
2
-
+
_______
/
6x
2
- 5x
Now compare the first term in the divisor and in the work below.
What would you multiply to x
to get 6x  ?
2
6x
+ 6x
Multiply 6x times each term in the divisor, then write the products under the  two terms below.
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
x
3
- 2x
2
-
+
_______
/
6x
2
- 5x
+ 6x
Multiply 6x times each term in the divisor, then write the products under the two terms below.
6x
2
- 12x
Change the signs before you combine like terms.
-
+
________
/
7x
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
x
3
- 2x
2
-
+
_______
/
6x
2
- 5x
+ 6x
6x
2
- 12x
-
+
________
/
7x
Bring down the next term.
+ 7
Now compare the first term in the divisor and in the work below.
What would you multiply to x
to get 7x?
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
x
3
- 2x
2
-
+
_______
/
6x
2
- 5x
+ 6x
6x
2
- 12x
-
+
________
/
7x
+ 7
Now compare the first term in the divisor and in the work below.
What would you multiply to x
to get 7x?
7
+ 7
Multiply 7 times each term in the divisor, then write the products under the  two terms below.
7x
- 14
Change the signs before you combine like terms.
Divide              x - 2   x  + 4x  - 5x + 7
3              2
)
________________
x
2
x
3
- 2x
2
-
+
_______
/
6x
2
- 5x
+ 6x
6x
2
- 12x
-
+
________
/
7x
+ 7
+ 7
7x
- 14
Change the signs before you combine like terms.
-
+
______
/
21
Add the remainder as a fraction.
+
21
___
x-2
NOW LET'S SEE
THE TRICKY PROBLEMS
Divide              
)
x + 2
x  + 5x + 4
3   
______________
Notice that the dividend is missing an x   term.
2
We have to insert
+ 0x    to complete the problem.
2
x  + 0x  + 5x + 4
3   
2
___________________
Divide              
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
After rewriting the dividend, 
you can finish the problem.
x
2
x
3
+ 2x
2
Divide              
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
After rewriting the dividend, 
you can finish the problem.
x
2
x
3
+ 2x
2
-
-
______
Divide              
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
After rewriting the dividend, 
you can finish the problem.
x
2
x
3
+ 2x
2
-
-
______
/
-2x
2
+ 5x
- 2x
-2x
2
+ 5x
Divide              
- 4x
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
After rewriting the dividend, 
you can finish the problem.
x
2
x
3
+ 2x
2
-
-
______
/
-2x
2
- 2x
-2x
2
+
+
_______
Divide              
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
After rewriting the dividend, 
you can finish the problem.
x
2
x
3
+ 2x
2
-
-
______
/
-2x
2
+ 5x
- 2x
-2x
2
- 4x
+
+
_______
/
9x
+ 4
+ 9
9x
+ 18
Divide              
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
After rewriting the dividend, 
you can finish the problem.
x
2
x
3
+ 2x
2
-
-
______
/
-2x
2
+ 5x
- 2x
-2x
2
- 4x
+
+
_______
/
9x
+ 4
+ 9
9x
+ 18
-
-
______
/
- 14
Divide              
)
x + 2
x  + 0x  + 5x + 4
3   
2
___________________
x
2
x
3
+ 2x
2
-
-
______
/
-2x
2
+ 5x
- 2x
-2x
2
- 4x
+
+
_______
/
9x
+ 4
+ 9
9x
+ 18
-
-
______
/
- 14
Since the remainder is negative,
you can subtract the remainder instead of adding it.
- 
14
___
x+2
Don't worry ... only one more!
Divide              
)
x - 4
x  + 5x - 4x - 20
3   
___________________
2
2
Notice that the divisor is missing an x term.
We have to insert
+ 0x  to finish the problem.
x  + 0x  - 4
2
After rewriting the divisor, 
you can complete the problem.
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
After rewriting the divisor, 
x
Notice we wrote x  over the third term.  
The divisor now has THREE terms, so we need to start our answer over the third term.
_____
you can complete the problem.
Continue completing the problem.
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
Continue completing the problem.
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
/
5x
2
/
+ 0x
Continue completing the problem.
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
/
5x
2
/
+ 0x
- 20
Continue completing the problem.
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
/
5x
2
/
+ 0x
- 20
+ 5
5x
2
+ 0x
- 20
-
-
+
__________
Continue  completing the problem.
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
/
5x
2
/
+ 0x
- 20
+ 5
5x
2
+ 0x
- 20
-
-
+
__________
/
Continue completing the problem.
/
/
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
/
5x
2
/
+ 0x
- 20
+ 5
5x
2
+ 0x
- 20
-
-
+
__________
0
Continue completing the problem.
There is no remainder, so the final answer is complete.
/
/
/
Divide              
)
x  + 5x - 4x - 20
3   
___________________
2
x  + 0x  - 4
2
x
x
3
+ 0x
2
- 4x
-
-
+
_________
/
5x
2
/
+ 0x
- 20
+ 5
5x
2
+ 0x
- 20
-
-
+
__________
/   /   /
0
Continue completing the problem.
There is no remainder, so the final answer is complete.
Thanks for Watching !
Thanks for Watching !

Polynomial Long Division

Copy this link to share with friends and colleagues:

WELCOME TO POWTOON!