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Math 9
Assignment Worksheet
Unit 8
Name:
Adding Polynomials
Add the polynomials by first grouping the like terms, then combining like terms.
Example
(4x + 7) + (3x – 2)
Group like terms: 4x + 3x + 7 – 2
Combine like terms: 7x + 5
1. (2x2 + 5x – 2 ) + (x2 – 2x + 5)
Group like terms:
Combine like terms:
2. (-y2 – 2y + 10) + (3y2 – 4y + 2)
Group like terms:
Combine like terms:
3. (5z + 5 – 2z2) + (5 – 6z + 3z2)
Group like terms:
Combine like terms:
4. (4x2 + 2x – 2) + (-x2 – 5x + 6)
Group like terms:
Combine like terms:
Add the polynomials by adding vertically:
5.
2x + 2
+ 4x - 5
6.
3x2 + 2x + 2
+ -x2 - 5x - 1
Page 1 of 8
Math 9
Assignment Worksheet
Unit 8
7. The left column represents ONE addition question. In the right column write symbolically
(using numbers and variables) the steps of the addition question that the model on the left
represents. See example in lesson 8a if necessary.
8. The model below represents the sum of 2 polynomials. What might the 2 polynomials be?
One possible answer would be: (2x2 + x – 1) + (-3x2 + x -1) = -x2 + 2x -2
9. Find the error in the following solution; then write out the correct solution.
2
2
Correct Solution
(3x – 6x + 3) + (-x – 3x + 4)
3x2 – 6x + 3 - x2 – 3x + 4
3x2 – x2 - 6x - 3x + 3 + 4
2x2 – 3x + 7
Page 2 of 8
Math 9
Assignment Worksheet
Unit 8
Subtracting Polynomials
Write the Additive Inverse for these expressions
10. -4x + 4x2 – 10
11. 5x2 – 10x + 7
12. – 2x2 – 5x + 5
13. 2m2 – 5m + 9
Subtract these polynomials by first converting to an addition question with the additive inverse.
Show each step.
Example:
(3x – 5) – (2x + 3)
Rewrite with additive inverse: (3x – 5) + (-2x + -3)
Group Like terms: 3x – 2x – 5 – 3
Combine Like terms: x – 8
14. (x + 7) – ( - x – 3)
Rewrite with additive inverse:
Group Like terms:
Combine Like terms:
15. (5x2 + 2x – 5) – (3x2 -2x + 6)
Rewrite with additive inverse:
Group Like terms:
Combine Like terms:
16. (y2 – 2y + 5) – (-2y2 + 6y -10)
Rewrite with additive inverse:
Group Like terms:
Combine Like terms:
Page 3 of 8
Math 9
Assignment Worksheet
Unit 8
17. (-5n2 +3n – 10) – (-2n2 – 4n + 7)
Rewrite with additive inverse:
Group Like terms:
Combine Like terms:
18. Find the error in the following solution; then write out the correct solution.
2
Correct Solution
2
(3x + 2x + 4) - (2x – 5)
3x2 + 2x + 4 - 2x2 + 5
x2 + 6x + 5
Express the perimeter of the given shape as a simplified polynomial:
19. Triangle
10b + 3
4b + 7
12b +15
20. Square
5x - 3
Page 4 of 8
Math 9
Assignment Worksheet
Unit 8
Multiplying Monomials by Monomials:
21. (3x) (5y)
24. (-5x)(-0.3y)
22. (-6a) (-4a)
25. (3abc) (-2abc)
23. (4b)(-3b)
26. 1/2b(8b)
4x
27. Write an expression to represent the area of this rectangle.
5x
28. What multiplication equation does this represent? (See lesson 8c)
29. Draw the algebra tiles that would represent the equation –3x(2x)
Page 5 of 8
Math 9
Assignment Worksheet
Unit 8
Multiplying Polynomials by Monomials:
30. 3x (2x – 1)
31. 4y(2y +1)
32. –3y (y - 2)
33. 3(m2 – 5m + 10)
34. -2b(3b – 2)
35. 3x(4x – 5x + 6)
36. 1/2r(2r + 5)
3x + 4
37. What would the area of this rectangle be
(as a simplified polynomial)?
x
Dividing Monomials by Monomials:
38. 6x ÷ 3
39. 32b ÷ - b
40. 25xy ÷ 5xy
41. -3.5a2 ÷ 7a2
Page 6 of 8
Math 9
Assignment Worksheet
Unit 8
42. 7ab ÷ -7ab
43. 17.3x2 ÷ x
44. w ÷ 3w
45. 12x2y2 ÷ 6x2y
Dividing Polynomials by Monomials:
46.
9x + 12
3
47.
14x - 2
2
48.
5x2 + 3x
x
49.
15b2 + 10b
5b
50.
6x2 + 3x - 12
3
51.
-18a2 – 12a
-6a
Page 7 of 8
Math 9
Assignment Worksheet
Unit 8
52. Given the area and one side length of the rectangle below, what is the length of the
unknown side? (Remember: to find the unknown side length you’ll need to use division)
?
3y
Area = 6y2 + 18y
53. Given the area and one side length of the rectangle below, what is the length of the
unknown side?
?
Area = 8x2 – 4x
2x
ANSWERS:
1. 2x2 + x2 + 5x – 2x – 2 + 5; 3x2 + 3x + 3; 3. 5z -6z + 5 + 5 + 3z2 – 2z2 ; -z + 10 + z2 ;
5. 6x – 3 7)4x + 7, ex – 2, 4x + 7 + 3x – 2; 7x + 5
9. 2x2 – 9x + 7 11. -5x2 + 10x – 7 13. -2m2 + 5m – 9
2
2
2
2
15. 5x + 2x – 5 + (– 3x ) + 2x – 6; 5x -3x + 2x + 2x – 5 – 6; 2x2 + 4x – 11
17. -5n2+ 3n – 10 + 2n2 + 4n – 7; -5n2 + 2n2 + 3n + 4n – 10 – 7; -3n2 + 7n – 17
19. 26b + 25 21. 15xy
23. -12b2
2 5. -6a2b2c2
2 7. (4x)(5x) = 20x2
2
2
2
2
31. 8y + 4y
33. 3m -15m + 30
35. -3x + 18x
37. 3x + 4x
39. -32 41. -0.5
43. 17.3x
45. 2y 47. 7x – 1
49. 3b + 2
51. 3a + 2
53. 4x - 2
Page 8 of 8