MAT 120
Homework 7
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor.
1) 24x2 - 120x + 150
A) (12x - 30)(2x - 5)
C) 6(4x2 - 20x + 25)
2) 0.25x 2 + 0.9x + 0.81
A) (0.5x2 + 0.9)2
D) 6(2x + 5)(2x - 5)
2)
B) (0.5x + 1.8)2
C) (0.25x + 0.81)2
3) 8pq4 - 8pr4
A) (8pq2 + pr2 )(pq2 - pr2)
C) 8p(q2 + r2 )(q2 - r2 )
4)
1)
B) 6(2x - 5)2
D) (0.5x + 0.9)2
B) (8pq2 + 8pr2 )(8pq2 - 8pr2)
D) 8p(q2 + r2 )(q + r)(q - r)
1
- p2
4
A)
1
1
+p
-p
4
4
3)
4)
B)
1
1
+p
-p
2
2
C)
5) mn 2 - 25m + 5n 2 - 125
A) (mn + 5)(n + 5m)(n + 5m)
C) (mn + 5)(n - 5)
1
1
-p
-p
2
2
D)
1
(1 + p)(1 - p)
4
B) (m + 5)(n - 5)
D) (m + 5)(n + 5)(n - 5)
6) 4c2 + 8cd + 4d2 - 64f2
B) 4((c + d)2 + 4f)((c + d)2 - 4f)
D) ((c + d)2 + 4f)((c + d)2 - 4f)
A) (c + d + 4f)(c + d - 4f)
C) 4(c + d + 4f)(c + d - 4f)
7) x3 - 216
A) (x - 6)(x2 + 6x + 36)
C) (x + 216)(x2 - 1)
B) (x - 6)(x2 + 36)
D) (x + 6)(x2 - 6x + 36)
Factor completely.
8) 48a 4b - 27b3
A) (12a + 9b)(4ab - 3b2)
C) 3b(4a2 + 3b)(4a2 - 3b)
B) 3b(4a + 3b)2
D) 3b(4a - 3b)2
9) t3 + 216
A) (t + 6)(t2 - 6t + 36)
C) (t - 6)(t2 + 6t + 36)
B) (t + 6)(t2 + 36)
D) (t - 216)(t2 - 1)
1
5)
6)
7)
8)
9)
Factor.
10) 64a 3 - 125b3
A) (64a - 5b)(a2 + 20ab + 25b2 )
B) (4a - 5b)(16a 2 + 20ab + 25b2 )
D) (4a - 5b)(16a 2 + 25b2 )
C) (4a + 5b2 )(16a2 - 20ab + 25b2)
Factor completely.
11) x2 + 3xy - 10y2
A) (x - 5y)(x + y)
B) (x - 5y)(x + 2y)
C) (x - y)(x + 2y)
12) 5x3 + 10x2 y - 75xy2
A) 5x(x + 3y)(x - 5y)
C) (5x2 + 15xy)(x - 5y)
13) 2x2 - 2x - 12
A) (2x + 4)(x - 3)
D) 5x(x - 3y)(x + 5y)
B) 2(x + 2)(x - 3)
C) (x + 2)(2x - 6)
D) 2(x - 2)(x + 3)
B) 2, 3
C) -2, -3
B) a = 2 or a = -8
C) a = 0 or a = 16
2
13)
14)
B) x(x3 - 1) - (x3 - 1)
D) x3 (x - 1) - (x - 1)
Solve the problem.
16) Given that g(x) = 6x + x2 ; find all values of a such that g(a) = 16.
A) a = -2 or a = 8
11)
12)
B) (x - 3y)(5x2 + 25xy)
14) x4 - x3 - x + 1
A) x4 - x3 - x + 1
C) (x - 1)2(x2 + x + 1)
Solve the equation.
15) 4x2 - 20x + 24 = 0
A) 4, 2, 3
D) (x + 5y)(x - 2y)
10)
D) 0, 2, 3
3
1
D) a = or a =
8
16
15)
16)
Use only the graph of f(x) = ax 2 + bx + c to find the x-intercepts of the graph and the solutions of the equation
ax 2 + bx + c = 0.
17) f(x) = -x2 + 5x - 6
17)
A) x-intercepts: (2, 0) and (3, 0)
solutions: -2, -3
C) x-intercepts: (2, 0) and (3, 0)
solutions: 2, 3
Solve.
B) x-intercepts: (0, 2) and (0, 3)
solutions: -2, -3
D) x-intercepts: (0, 2) and (0, 3)
solutions: 2, 3
18) Find three consecutive integers such that the square of the sum of the smaller two is 105 more than
the square of the largest.
A) -6, -5, -4
B) 6, 7, 8, or -6, -5, -4
C) 6, 7, 8
D) 4, 6, 8
18)
19) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 feet. Find
the length of the ladder if the length is 4 feet more than its distance from the wall.
A) 20 feet
B) 24 feet
C) 16 feet
D) 12 feet
19)
20) If an object is thrown upward with an initial velocity of 96 ft/sec, its height after t sec is given by h =
96t - 16t2 . Find the number of seconds before the object hits the ground.
20)
A) 3 sec
B) 48 sec
C) 80 sec
3
D) 6 sec