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.

2×2 + 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. 15×2 – 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
4×2+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
3×2-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. 9×2 + 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