1. Write the dividend and divisor with the divisor outside the long division bar. 2. Divide the first term of the dividend by the divisor and write the result above the division bar. 3. Multiply the divisor by the result and write the product below the terms of the dividend. 4. Subtract to find the remainder and bring down the next term to continue the process until there is no remainder. This document explains how to perform long division of polynomials using the same process as long division of numbers. It provides an example of performing long division step-by-step to divide a quadratic polynomial by a linear polynomial.

1. Polynomial Division
Dividing a Monomial by a Monomial
Long Division
Synthetic Division

2. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents:

3. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents:
Like bases, subtract smaller from
the larger exponent to get the
new exponent and keep the same
base.

4. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents:
Like bases, subtract smaller from
the larger exponent to get the
new exponent and keep the same
base.
If the larger exponent is in the
numerator, the result goes in the
numerator.

5. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
base.
If the larger exponent is in the
numerator, the result goes in the
numerator.

6. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the
numerator.

7. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the 2
numerator. =x

8. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
Like bases, subtract smaller from 3
the larger exponent to get the
x
new exponent and keep the same
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the 2
numerator. =x
If the larger exponent is in the
denominator, the result goes in
the denominator.

9. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
a4
Like bases, subtract smaller from 3 9
the larger exponent to get the
x a
new exponent and keep the same
base. =x 5− 3
If the larger exponent is in the
numerator, the result goes in the 2
numerator. =x
If the larger exponent is in the
denominator, the result goes in
the denominator.

10. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
a 4
Like bases, subtract smaller from 3 9
the larger exponent to get the
x a
new exponent and keep the same
base. =x 5− 3 1
= 9− 4
If the larger exponent is in the a
numerator, the result goes in the 2
numerator. =x
If the larger exponent is in the
denominator, the result goes in
the denominator.

11. Dividing a Monomial by a Monomial
Apply the rules for dividing
exponents: x 5
a 4
Like bases, subtract smaller from 3 9
the larger exponent to get the
x a
new exponent and keep the same
base. =x 5− 3 1
= 9− 4
If the larger exponent is in the a
numerator, the result goes in the 2
numerator. =x
1
If the larger exponent is in the = 5
denominator, the result goes in a
the denominator.

12. Simplify.
5 3
8a b
2 7
6a b

13. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
6 by 2.

14. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b

15. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b
Apply the rules for
dividing powers
with like bases.

16. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b
Apply the rules for
4a 5−2
dividing powers
7− 3 with like bases.
3b

17. Simplify.
5
8a b 3
Reduce the
2 7 numerical part by
6a b
dividing the 8 and
4
8a b 5 3
6 by 2.
2 7
3 6a b
Apply the rules for
4a 5−2
dividing powers
7− 3 with like bases.
3b
3 And you are done
4a
4
dividing a monomial
3b by a monomial.

18. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk

19. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 2 −1
12 f
= 10 − 8
5 30 d

20. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 2 −1
12 f
= 10 − 8
5 30 d
2f
= 2
5d

21. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 3
12 f 2 −1
27 j
= 10 − 8
= 9− 3 9−5
5 30 d 1 9h jk
2f
= 2
5d

22. Simplify each of the following.
8 2 3 5
12d f 27h jk
10 9 9
30d f 9h jk
2 3
12 f 2 −1
27 j
= 10 − 8
= 9− 3 9−5
5 30 d 1 9h jk
2f 3
= 2 = 6 4
5d h k

23. Algebra Cruncher Problems
Follow this link to try a couple on your own at Cool Math.
Notice when you select the “Give me a Problem” button
to try new problems, 2 rows are generated. Look
carefully between them. That red line indicates this
problem is a fraction.
Do your work in a notebook before entering your answer.
When you select “What’s the Answer?” compare your
answer with the given answer.
Keep selecting new problems until you get 3
consecutive problems correct.

24. Divide a Polynomial by a Monomial
Visit this Cool math website to learn about dividing
a Polynomial by a monomial.
Be sure to click the “next page” to review the 2
pages of notes.
Complete the “Try it” problem on page 2 in your
notebook.

25. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2

26. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2
2 2
4wy 20w 6wy 7
= 2
− 2
+ 2
− 2
4wy 4wy 4wy 4wy

27. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2
2 2
4wy 20w 6wy 7
= 2
− 2
+ 2
− 2
4wy 4wy 4wy 4wy
2 5 2 −1 3
4wy 20 w 6w 7
= − 2
+ 2 −1
− 2
4wy 2
1 4y 2 4 wy 4wy

28. Try It - Page 2
( 4wy − 20w + 6wy − 7 ) ÷ 4wy
2 2 2
2 2
4wy 20w 6wy 7
= 2
− 2
+ 2
− 2
4wy 4wy 4wy 4wy
2 5 2 −1 3
4wy 20 w 6w 7
= − 2
+ 2 −1
− 2
4wy 2
1 4y 2 4 wy 4wy
5w 3 7
= 1− 2 + − 2
y 2y 4wy

29. It’s Practice time...
Go to the Regents Prep website to
practice dividing a polynomial by a
monomial. Only practice questions 1
through 7!
Message or Pronto me if you have
questions.

30. Polynomial Long Division
Polynomial long division is essentially the same as
long division for numbers. This method can be used
to write an improper polynomial as the sum of a
polynomial with a remainder.

31. Polynomial Long Division
Polynomial long division is essentially the same as
long division for numbers. This method can be used
to write an improper polynomial as the sum of a
polynomial with a remainder.
You can also use polynomial division to help you
factor polynomials completely. Just as we can
divide 56 by 7, we can divide x2 + 4x – 32 by x + 8.

32. Polynomial Long Division
Polynomial long division is essentially the same as
long division for numbers. This method can be used
to write an improper polynomial as the sum of a
polynomial with a remainder.
You can also use polynomial division to help you
factor polynomials completely. Just as we can
divide 56 by 7, we can divide x2 + 4x – 32 by x + 8.
Explore Long Division here by viewing this video.

33. Let’s try one together!
( x + 3x − 12 ) divided by ( x − 3)
2
2
The expression x + 3x – 12 is called the dividend
and the expression x -3 is called the divisor.

34. Let’s try one together!
( x + 3x − 12 ) divided by ( x − 3)
2
2
The expression x + 3x – 12 is called the dividend
and the expression x -3 is called the divisor.
Divisor goes outside the division bar.

35. Let’s try one together!
( x + 3x − 12 ) divided by ( x − 3)
2
2
The expression x + 3x – 12 is called the dividend
and the expression x -3 is called the divisor.
Divisor goes outside the division bar.
2
x−3 x + 3x − 12

36. 2
x−3 x + 3x − 12

37. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x
2
x−3 x + 3x − 12

38. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
2
x−3 x + 3x − 12

39. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!

40. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
( 2
− x − 3x )

41. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
( 2
− x − 3x )
6x

42. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x

43. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12

44. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?

45. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x +6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?

46. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x +6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?
Multiply the divisor again and write it
under the portion left over from
before.

47. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x +6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?
Multiply the divisor again and write it
− ( 6x − 18 )
under the portion left over from
before. 6

48. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x +6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?
Multiply the divisor again and write it
− ( 6x − 18 )
under the portion left over from
before. 6
When you are out of terms to bring
down, the last number is the
remainder.

49. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x + 6 R6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?
Multiply the divisor again and write it
− ( 6x − 18 )
under the portion left over from
before. 6
When you are out of terms to bring
down, the last number is the
remainder.

50. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x + 6 R6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?
Multiply the divisor again and write it
− ( 6x − 18 )
under the portion left over from
before. 6
When you are out of terms to bring
down, the last number is the
remainder.
Write your final answer as a sum with
the remainder written over the divisor.

51. Start by doing monomial by monomial
division. Divide the 1st term of the
dividend an divisor. x2/x = x x + 6 R6
Write the product under the terms in
the dividend. Then subtract the 2
product from the portion above it. x −3 x + 3x − 12
Watch your signs!
Next, bring down the next term in the
( 2
− x − 3x )
dividend.
6x −12
Repeat the same steps. What is 6x/x?
Multiply the divisor again and write it
− ( 6x − 18 )
under the portion left over from
before. 6
When you are out of terms to bring
down, the last number is the
remainder. 6
x+6+
Write your final answer as a sum with x−3
the remainder written over the divisor.

52. Try this one on your own...
( x + 3x − 6x − 7 ) ÷ ( x + 4 )
3 2
Clip art licensed from the Clip Art Gallery on DiscoverySchool.com

53. 2 1
Final answer: x − x − 2 +
x+4
2
x −x −2 R1
3 2
x+4 x +3x −6x −7
3 2
− (x +4x )
2
−x −6x
2
− (−x −4x)
−2x −7
− (−2x −8)
1

54. Need more work with long division?
Follow this link to the MathIsFun website to see
more examples of long divison

55. Synthetic Division
We also have a simplified method called Synthetic
Division that takes away the variables and the
messy subtraction!
Watch this video on Synthetic Division and be
amazed!

56. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)

57. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.

58. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
x−3= 0
x=3

59. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
x=3

60. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
x=3
3

61. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
3

62. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
3 1 3 −12

63. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12

64. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
1

65. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
first coefficient and place the product
under the next coefficient. 1

66. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3
first coefficient and place the product
under the next coefficient. 1

67. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3
first coefficient and place the product
under the next coefficient. 1
6. Add down and repeat the process.

68. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3
first coefficient and place the product
under the next coefficient. 1 6
6. Add down and repeat the process.

69. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3 18
first coefficient and place the product
under the next coefficient. 1 6
6. Add down and repeat the process.

70. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3 18
first coefficient and place the product
under the next coefficient. 1 6 6
6. Add down and repeat the process.

71. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3 18
first coefficient and place the product
under the next coefficient. 1 6 6
6. Add down and repeat the process.
7. Write your polynomial starting with 1 less
degree than your divisor. The last digit
will be your remainder.

72. See our long division example using synthetic division!
(x2 + 3x – 12) divided by (x – 3)
1. Set the divisor equal to zero and solve.
2. Put that number in a box in the top left
corner.
x−3= 0
3. List the coefficients of the dividend in x=3
order from left to right.
4. Drop the first coefficient.
3 1 3 −12
5. Multiply the number in the box by the
3 18
first coefficient and place the product
under the next coefficient. 1 6 6
6. Add down and repeat the process.
6
7. Write your polynomial starting with 1 less x+6+
degree than your divisor. The last digit x−3
will be your remainder.

73. You try!
x + 3x - 6x – 7
3 2
divided by
x+4

74. You try! Find the number for
the box.
x + 3x - 6x – 7
3 2
divided by
x+4

75. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
divided by
x+4

76. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
divided by −4
x+4

77. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4
x+4

78. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4 1 3 −6 −7
x+4

79. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4 1 3 −6 −7
x+4 1

80. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4 1 3 −6 −7
−4
x+4 1 −1

81. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4 1 3 −6 −7
−4 4
x+4 1 −1 −2

82. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4 1 3 −6 −7
−4 4 8
x+4 1 −1 −2 1

83. You try! Find the number for
the box.
x+4=0
x + 3x - 6x – 7
3 2 x = −4
Coefficients.
divided by −4 1 3 −6 −7
−4 4 8
x+4 1 −1 −2 1
2 1
Final Answer: x − x − 2 +
x+4

84. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.

85. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8

86. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
1

87. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4
1

88. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4
1 −4

89. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4 16
1 −4

90. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4 16
1 −4 2

91. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4 16 −8
1 −4 2

92. (
Try this one...
3
) (
x − 14x + 8 ÷ x + 4 )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4 16 −8
1 −4 2 0

93. Try this one... ( 3
x − 14x + 8 ÷ x + 4) ( )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4 16 −8
1 −4 2 0
The remainder is 0 so it’s not included in the
result.

94. Try this one... ( 3
x − 14x + 8 ÷ x + 4 ) ( )
Notice the x2 term is missing. You
need to account for this term when
setting up your division.
−4 1 0 −14 8
−4 16 −8
1 −4 2 0
2
x − 4x + 2
The remainder is 0 so it’s not included in the
result.

95. Shall we Play a GAME?
Check your knowledge on Dividing Polynomials by
playing Jeopardy. Ok, technically it’s called
Challenge Board but it’s the same idea! There are
4 categories: horseshoes, handgrenades, doesn’t
count, and polynomial long division.
You have the option to play alone or against a
friend or family member.
You could even arrange a time with a classmate to
meet on Pronto to play. Try the App Share feature
to see the same game board!

96. Remainder Theorem
If the polynomial P(x) of degree n ≥ 1
is divided by (x –a), where a is a constant,
then the remainder is P(a).

97. Remainder Theorem
If the polynomial P(x) of degree n ≥ 1
is divided by (x –a), where a is a constant,
then the remainder is P(a).
In English, this means we can use
the remainder theorem to
evaluate a function for a
specific value. See it in action…

98. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2

99. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10

100. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
3

101. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6
3

102. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6
3 −11

103. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6 22
3 −11

104. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6 22
3 −11 29

105. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6 22 −58
3 −11 29

106. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6 22 −58
3 −11 29 −68

107. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6 22 −58
3 −11 29
Therefore, f(-2) is −68

108. Evaluate the function using the remainder
theorem.
f ( x ) = 3x − 5x + 7x − 10 at x = −2
3 2
−2 3 −5 7 −10
−6 22 −58
3 −11 29
Therefore, f(-2) is −68
Don’t believe it? Check it out in your calculator.

109. Congratulations!
You’ve finished the notes and practice
for Polynomial Division.
You are now ready to proceed to the
Assignment.
Good luck!