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

1. **Question: **Factor the trinomial completely.

s^{2} + 5s + 66

**Question:**Solve.

v^{2} – 30v + 29 = 0

**Question:**Factor by grouping.

x^{3} + 5x^{2} + 6x + 30

__ __

x^{3} + 5x^{2} + 6x + 30 = (x + 5)(x^{2} + 6)

**Question:**Complete the factoring.

2x^{3} + 14x^{2} + 24x

**Question:**Complete the factoring.

12a^{3} – 26a^{2} + 4a = 2a(__ _)__

= 2a(__ ) ( )__

**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?**Question:**Factor the trinomial.

## STATUS

r^{2} + 6r + 5

**Question:**Factor the following polynomial by grouping.

s^{2} + 11sg + 28g^{2}

**Question:**Solve using the zero factory property.

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

**Question:**Factor completely.

64s^{2} + 25g^{2}

**Question:**Factor the trinomial by grouping.

8m^{2} – 2m – 3

**Question:**Factor completely.

s^{2} + 4

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

a^{2} – 16, y^{2} + 4, 8m^{2 }– 25, 9x^{2} – 1

**Question:**Factor the special product.

25r^{2} – 30r + 9

**Question:**Find the greatest common factor (GCF) of 24x and 9.**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.

**Question:**If an object is projected upward with an initial velocity of 128 ft per sec, its height h after t second is h = -6t^{2}+ 128t. Find the height of the object after 4 seconds.**Question:**What polynomial can be factored as (a + 9)(a + 5).**Question:**Factor. Note that the middle term has already been split.

40r^{2} – 35r + 24r – 21

__ __

40r^{2} – 35r + 24r – 21 = (5r + 3)(8r – 7)

**Quesution:**Factor completely.

36x^{2} – 84xy + 49y^{2}

**Question:**Complete the factoring.

2a^{2} + 4a – 16 = 2( )( )

__ __

2a^{2} + 4a – 16 = 2(a – 2)(a + 4)

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

10r^{2} + 31rs + 15s^{2} = 10r^{2} + 25rs + 6rs + 15s^{2}

__ __

10r^{2} + 25rs + 6rs + 15s^{2 }= (2r + 5s)(5r + 3s)

**Question:**Complete the factoring.

2y + 30 = 2( )

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

20b^{2} + 5b

**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.**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.**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
**. 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. **Question:**Which of the following are differences of squareds?

a^{2 }– 16, y^{2} + 4, 8m^{2} – 25, 9x^{2} – 1