Download Unit 5 Review Worksheet

Name: ________________________ Class: ___________________ Date: __________
Math 10 - Unit 5 REVIEW WORKSHEET- Polynomials
ID: A
NO CALCULATORS
Multiple Choice
Identify the choice that best answers the question.
1. Factor the trinomial −49x 5 y 6 − 28x 4 y 5 − 63x 3 y 7 .
5. Expand and simplify: (2x 2 + 3x − 6)(5x 2 − 2x + 3)
a. −7x 3 y 5 (7x 2 y + 4x + 9y 2 )
a.
b.
c.
d.
b. −7x 3 (7x 2 y 6 + 4xy 5 + 9y 7 )
c. 7x 4 y 5 (−7xy − 4 − 9y 2 )
d. −3.5x 3 y 5 (14x 2 y + 8x + 18y 2 )
10x 4 + 11x 3 − 30x 2 + 21x − 18
10x 4 + 11x 3 − 30x 2 − 3x + 18
10x 4 + 11x 3 − 24x 2 + 21x + 18
10x 4 − 19x 3 − 30x 2 + 21x − 18
6. Expand and simplify: (4x 2 + 3x − 6)(5x 2 − 2x + 3)
2. Factor the trinomial −56x 5 y 6 − 32x 4 y 5 − 72x 3 y 7 .
a.
b.
c.
d.
a. −8x 3 y 5 (7x 2 y + 4x + 9y 2 )
b. −8x 3 (7x 2 y 6 + 4xy 5 + 9y 7 )
c. 8x 4 y 5 (−7xy − 4 − 9y 2 )
d. −4x 3 y 5 (14x 2 y + 8x + 18y 2 )
20x 4 + 7x 3 − 24x 2 + 21x − 18
20x 4 + 7x 3 − 24x 2 − 3x + 18
20x 4 + 7x 3 − 18x 2 + 21x + 18
20x 4 − 23x 3 − 24x 2 + 21x − 18
7. Expand and simplify: (3m − 5n) 3
3. Which polynomial, written in simplified form,
represents the area of this rectangle?
a. 27m3 − 135m2 n + 225mn 2 − 125n 3
b. 9m3 − 15mn + 25n 3 c. 9m3 − 25n 3
d. 9m3 − 30mn + 25n 3
8. Expand and simplify: (5m − 2n) 3
a. 125m3 − 225m2 n + 135mn 2 − 27
b. 125m3 − 150m2 n + 60mn 2 − 8n 3
c. 125m3 − 8n 3 d. 125m3 − 30mn + 8n 3
a. 4x 2 − 30xy − 54y 2 b. 4x 2 + 21xy − 54y 2
9. Expand and simplify: (6p + 1)(3p − 6)
c. 4x 2 + 30xy − 54y 2 d. 8x 2 + 60xy − 108y 2
a. 18p 2 − 39p − 6 b. 18p 2 + 39p − 6
4. Which polynomial, written in simplified form,
represents the area of this rectangle?
c. 18p 2 − 33p − 6 d. 18p 2 + 33p − 6
10. Expand and simplify: (8p + 3)(5p − 6)
a. 40p 2 − 63p − 18 b. 40p 2 + 63p − 18
c. 40p 2 − 33p − 18 d. 40p 2 + 33p − 18
a. 8x 2 − 70xy − 18y 2 b. 8x 2 + 37xy − 18y 2
c. 8x 2 + 70xy − 18y 2 d. 16x 2 + 140xy − 36y 2
1
Name: ________________________
ID: A
11. Which set of algebra tiles represents x 2 + 2x + 3 ?
14. Expand and simplify: (7m − 5n) 2
a. 49m2 − 35mn + 25n 2 b. 49m2 + 25n 2
c. 49m2 − 25n 2 d. 49m2 − 70mn + 25n 2
15. Expand and simplify:
(4p + 5)(3p − 5) − (3p − 4)(p − 3)
a. 9p 2 + 8p − 13 b. 9p 2 − 18p − 37
a.
c. 9p 2 − 18p − 13 d. 9p 2 + 8p − 37
16. Expand and simplify: (p + 2)(p − 8)
a. p 2 − 10p − 16 b. p 2 + 6p − 16
c. p 2 − 6p − 16 d. p 2 + 10p − 16
b.
17. Identify the greatest common factor of the terms in
the trinomial 4s 3 t 4 + 8s 4 t 2 − 10s 2 t 3 .
a. 4s 2 t 2 b. 2s 2 t 3 c. 2s 3 t 2 d. 2s 2 t 2
18. Identify the greatest common factor of the terms in
the trinomial 14s 3 t 4 + 28s 4 t 2 − 35s 2 t 3 .
a. 14s 2 t 2 b. 7s 2 t 3 c. 7s 3 t 2 d. 7s 2 t 2
c.
19. Expand and simplify: (6x − y)(2x + 8y) − (2x − 5y) 2
a. 8x 2 + 26xy + 17y 2 b. 8x 2 + 66xy − 33y 2
c. 8x 2 + 66xy + 17y 2 d. 8x 2 + 56xy − 33y 2
d.
20. Expand and simplify: (8h + 3)(7h 2 − 4h + 1)
12. Each shape is a rectangle. Write a polynomial, in
simplified form, to represent the area of the shaded
region.
a. 56h 3 − 11h 2 − 4h + 3 b. 56h 3 − 53h 2 − 20h + 3
c. 56h 3 + 11h 2 − 12h + 3 d. 56h 3 − 32h 2 + 8h + 3
21. Expand and simplify: (6h + 1)(7h 2 − 4h + 1)
a. 42h 3 − 17h 2 + 2h + 1 b. 42h 3 − 31h 2 − 10h + 1
c. 42h 3 + 17h 2 − 4h + 1 d. 42h 3 − 24h 2 + 6h + 1
22. Identify this polynomial as a perfect square
trinomial, a difference of squares, or neither.
25g 2 − 9h 2
a. Difference of squares b. Neither c. Perfect
square trinomial
a. 5x 2 + 35x + 32 b. 5x 2 + 35x + 52
c. 5x 2 + 29x + 32 d. 5x 2 + 29x + 52
13. Expand and simplify: (9m − 2n) 2
a. 81m2 − 18mn + 4n 2 b. 81m2 + 4n 2
c. 81m2 − 4n 2 d. 81m2 − 36mn + 4n 2
2
Name: ________________________
ID: A
24. Which multiplication sentence does this set of
algebra tiles represent?
23. Which multiplication sentence does this set of
algebra tiles represent?
a. (2x − 2)(2x + 2) b. (2x + 2)(2x + 2)
2
2
2
a. (2x − 1)(2x − 1) b. (2x + 1)(2x + 1)
2
c. (2x 2 + x)(2x 2 + x) d. (2x 2 + 1)(2x 2 + 1)
c. (2x + 2x)(2x + 2x) d. (2x + 2)(2x + 2)
Short Answer Please clearly show your process and box your final answer for full marks. Remember proper form!
25. Factor fully: p 2 − 100
36. Factor fully: 81s 2 − 16t 2
26. Factor fully: q 2 + 25
37. Factor fully: 64h 2 − 32h + 4
27. Factor fully: 25x 3 − 140x.
38. Factor fully: 4p 4 + 12p 2 + 9
28. Factor fully: 51x 3 − 48x.
39. Factor fully: 36a 4 − 31a 2 + 3
29. Factor fully: 18p 4 − 12p 2 + 2
40. Factor fully: 2p 4 − 3p 2 − 20
30. Factor fully: −64x 4 − 224x 2 − 196
41. Factor fully: 25z 2 − 80z + 55
31. Write an example of a perfect square trinomial.
42. Factor fully: 9z 2 − 30z + 21
32. Write an example of a difference of squares.
43. Factor fully: s 2 − 34s + 33
33. Factor fully: a 4 − 10000
44. Factor fully: s 2 − 27s + 26
34. Factor fully: 16x 8 − 1
45. Factor fully: 22n 2 + n − 5
35. Factor fully: 9s 2 − 16t 2
46. Factor fully: 14n 2 + n − 3
3
Name: ________________________
ID: A
Problem
47. Write an expression for the width of this rectangle.
48. Multiply this pair of binomials. Sketch and label an
area model to illustrate the product.
(x + 7 ) (x − 1 )
49. Multiply this pair of binomials. Sketch and label an
area model to illustrate the product.
(x + 8 ) (x − 1 )
4
ID: A
Math 10 - Unit 5 REVIEW WORKSHEET- Polynomials
Answer Section
MULTIPLE CHOICE
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24.
A
A
C
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A
B
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B
A
A
A
B
B
SHORT ANSWER
25. ÊÁË p + 10 ˆ˜¯ ÊÁË p − 10 ˆ˜¯
26. Not factorable
27. 5x(5x 2 − 28)
28. 3x(17x 2 − 16)
Ê
ˆ2
29. 2 ÁÁ 3p 2 − 1 ˜˜
Ë
¯
Ê
ˆ2
30. −4 ÁÁ 4x 2 + 7 ˜˜
Ë
¯
31. Answers will vary. Example: x 2 − 8x + 16
32. Answers will vary. Example: x 2 − 9
1
NO CALCULATORS
ID: A
Ê
ˆ
33. ÁÁ a 2 + 100 ˜˜ (a + 10) (a − 10)
Ë
¯
ÊÁ 4
ˆ˜ ÊÁ 2
ˆÊ
ˆ
34. Á 4x + 1 ˜ Á 2x + 1 ˜˜ ÁÁ 2x 2 − 1 ˜˜
Ë
¯Ë
¯Ë
¯
35. (3s + 4t ) (3s − 4t )
36. (9s + 4t ) (9s − 4t )
2
37. (8h − 2)
Ê
ˆ2
38. ÁÁ 2p 2 + 3 ˜˜
Ë
¯
Ê 2
ˆ
Á
˜
39. Á 4a − 3˜ (3a + 1) (3a − 1)
Ë
¯
ÊÁ 2
ˆ˜ ÊÁ
40. Á 2p + 5 ˜ Ë p + 2ˆ˜¯ ÊÁË p − 2 ˆ˜¯
Ë
¯
41. 5 (5z − 11) ( z − 1)
42. 3 (3z − 7) ( z − 1)
43. (s − 33) (s − 1)
44. (s − 26) (s − 1)
45. (11n − 5) (2n + 1)
46. (7n − 3) (2n + 1)
PROBLEM
47. a + 4b
48.
(x + 7 ) (x − 1 ) = x 2 + (−1x) + 7x + (−7)
= (x 2 + 6x − 7)
49.
(x + 8 ) (x − 1 ) = x 2 + (−1x) + 8x + (−8)
= (x 2 + 7x − 8)
2