MATH 114N Week 3 Test 1 Review Attempt 1 | Solutions

1. Question: Factor the trinomial completely.

s²  + 5s + 66

2. Question: Solve.

v² – 30v + 29 = 0

3. Question: Factor by grouping.

x³ + 5x² + 6x + 30      ­­­­­

x³ + 5x² + 6x + 30 = (x + 5)(x² + 6)

4. Question: Complete the factoring.

2x³ + 14x² + 24x

5. Question: Complete the factoring.

12a³ – 26a² + 4a = 2a(                         _)

= 2a(      ) (      )

6. Question: Mary works due north of home. Her husband Juan works due east. They leave for work at the same time. By the time Mary is 5 miles from home, the distance between them is one mile more than Juan’s distance from home. How far from home is Juan?
7. Question: Factor the trinomial.

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r² + 6r + 5

8. Question: Factor the following polynomial by grouping.

s² + 11sg + 28g²         ­­­­­

9. Question: Solve using the zero factory property.

(2w + 5)(w + 4) = 0

10. Question: Factor completely.

64s² + 25g²

11. Question: Factor the trinomial by grouping.

8m² – 2m – 3

12. Question: Factor completely.

s² + 4

13. Question: Which of the following are differences of square.

a² – 16, y² + 4, 8m² – 25, 9x² – 1

14. Question: Factor the special product.

25r² – 30r + 9

15. Question: Find the greatest common factor (GCF) of 24x and 9.
16. Question: The area of parallelogram is given by the A = bh.

The area of parallelogram on the right side is 45 sq.units.

Find its base and height.

17. Question: If an object is projected upward with an initial velocity of 128 ft per sec, its height h after t second is h = -6t² + 128t. Find the height of the object after 4 seconds.
18. Question: What polynomial can be factored as (a + 9)(a + 5).
19. Question: Factor. Note that the middle term has already been split.

40r² – 35r + 24r – 21   ­­­­­

40r² – 35r + 24r – 21 = (5r + 3)(8r – 7)

20. Quesution: Factor completely.

36x² – 84xy + 49y²

21. Question: Complete the factoring.

2a² + 4a – 16 = 2(     )(    )      ­­­­­

2a² + 4a – 16 = 2(a – 2)(a + 4)

22. Question: The middle term of the trinomial has been rewritten. Now factor by grouping.

10r² + 31rs + 15s² = 10r² + 25rs + 6rs + 15s²  ­­­­­

10r² + 25rs + 6rs + 15s² = (2r + 5s)(5r + 3s)

23. Question: Complete the factoring.

2y + 30 = 2(      )

24. Question: The product of two consecutive integers is 1 more than their sum. Find the integers.
25. Question: Factor.

20b² + 5b

26. Question: A garden has a shape of a right triangle with one leg of 8 meters longer than the other. The hypotenuse is 8 meters less than twice the length of the shorter leg. What is the length of the shorter leg.
27. Question: A garden has a shape of a right triangle with one leg of 6 meters longer than the other. The hypotenuse is 6 meters less than twice the length of the shorter leg. What is the length of the shorter leg.
28. Question: A garden has a shape of a right triangle with one leg of 4 meters longer than the other. The hypotenuse is 4 meters less than twice the length of the shorter leg. What is the length of the shorter leg.
29. 29. Question: A garden has a shape of a right triangle with one leg of 2 meters longer than the other. The hypotenuse is 2 meters less than twice the length of the shorter leg. What is the length of the shorter leg.
30. Question: Which of the following are differences of squareds?

a² – 16, y² + 4, 8m² – 25, 9x² – 1