ALLIED MAT110 MODULE 4 CHECK YOUR UNDERSTANDINGS

Question Points

1. Solve the quadratic equation. 3x(2x – 5) = 75

a. 0,

b. 0, -

c. 5, -

d. –5,

1

2. Subtract. Express your answer in simplest form.

a.

b.

c. 2

d.

1

3. The GCF of 6y + 3 is 3. The GCF of 10y + 12 is 2. Find the GCF of the product (6y + 3)(10y + 12).

a. 1

b. 30

c. 6

d. 5

1

4. Determine whether the following trinomial is a perfect square. If it is, factor the binomial. x2 + 9x + 9

a. Yes; (x + 3)2

b. Yes; (x – 3)2

c. Yes; (x + 9)2

d. No

1

5.

State which method should be applied as the first step for factoring the polynomial.

2x2 + 5xy + 2x + 5y

a. Find the GCF.

b. Group the terms.

c. Factor the difference of squares.

d. Use the ac method (or trial and error).

1

6. Solve for x.

a. –2

b. 2

c. –4

d. No solution

7.

What values for x, if any, must be excluded in the following algebraic fraction?

a.

b.

c.

d.

1

8. State which method should be applied as the first step for factoring the polynomial. (x + 9y)2 – 1

a. Find the GCF.

b. Group the terms.

c. Factor the difference of squares.

d. Use the ac method (or trial and error).

9. One number is 8 more than another. Let x represent the larger number and use a rational expression to represent the sum of the reciprocals of the two numbers.

a. 1

b.

c.

d.

1

10. Multiply.

a.

b.

c.

d.

1

11. The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2 – 23h + 45. Write this polynomial in factored form.

a. (hh + 5)(2h + 9)

b. (hh – 5)(2h – 9)

c. (2hh – 5)(h – 9)

d. (2hh + 5)(h + 9)

1

12. Find a positive value for k for which the polynomial can be factored. x2 – kx + 23

a. 1

b. 22

c. 23

d. 24

1

13. Factor completely. 15x2 – 16x + 4

a. (3x – 2)(5x – 2)

b. (3x + 2)(5x + 2)

c. (15x – 2)(x – 2)

d. (3x + 1)(5x + 4)

1

14. Factor 4x2+5x-6

a. (4x-3)(x+2)

b. (4x-3)(x-2)

c. (4x+3)(x+2)

d. (4x+3)(x-2)

1

15. The area of a rectangle of length t is given by 12t – t2. Find the width of the rectangle in terms of t.

a. 12 – t

b. 12t

c. t – 12

d. t2

16. Factor 3x2-x-4

a. (3x-4)(x+1)

b. (3x+4)(x+1)

c. (3x-4)(x-1)

d. (3x+4)(x1)

1

17. During rush hour, Fernando can drive 25 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.

a. 36

b. 38

c. 45

d. 47

18. Factor completely. x2 + x – 42

a. (x – 1)(x + 42)

b. (x + 1)(x – 42)

c. (x + 6)(x – 7)

d. (x – 6)(x + 7)

1

19. Solve the quadratic equation. x2 = –6x

a. 0, –6

b. 0, 6

c. 6, –6

d. 2, 6

1

20. Solve for x.

a. 8

b.

c. 32

d.

1

21. Multiply.

a.

b.

c. –n2 + n

d. 3

22. Factor completely. 9x2 + 30xy + 25y2

a. (3x + 5y)2

b. (3x – 5y)(3x + 5y)

c. (9x + 5y)(x + 5y)

d. (3x + y)(3x + 25y)

1

23. Add or subtract as indicated.

a.

b.

c.

d.

0

24. Write in simplest form.

a.

b.

c. 4a4b

d.

1

25. What values for x, if any, must be excluded in the following algebraic fraction?

a. 0

b. –6

c. 6

d. None

1

26. Factor the trinomial completely.. 6b4 – 18b3 – 60b2

a. 6b2(b + 2)(b – 5)

b. 6b2(b – 2)(b + 5)

c. 6(b2 + 2)(b2 – 5)

d. b2(2b + 5)(3b + 10)

27. Write the expression in simplest form.

a.

b. -

c. -

d.

28. Factor out the GCF with a negative coefficient. –40p2q5 + 24pq4 – 40q3

a. –8(5p2q5 + 3pq4 – 5q3)

b. –8(5p2q5 – 3pq4 + 5q3)

c. –8q3(5p2q2 – 3pq + 5)

d. –8q3(5p2q2 + 3pq – 5)

1

29.

Perform the indicated operations.

a.

b.

c.

d.

1

30. Solve for x. + 7 = 7

a. 0

b. 35

c. 49

d. 84