Draw and label rectangles to illustrate the given product.
259)
x(x + 3)
A)
B)
C)
D)
260)
(2x + 5)(2x + 5)
A)
B)
C)
D)
Multiply.
261)
(x2– x +9)(x +4)
A)
x3+36
B)
x3+5x2+13x +36
C)
D)
x3+3x2+5x +36
Answer:
D
262)
(x –5)(9x2+ x +8)
A)
9x3–44x2+13x –40
B)
9x3+44x2+3x –40
C)
9x3–46x2+3x –40
D)
9x3–44x2+3x –40
Answer:
D
263)
(4p – 1)(16p2+ 4p + 1)
A)
64p3+ 20p2– 1
B)
64p3– 1
C)
D)
16p3– 1
Answer:
B
264)
(4y – 5)(16y2+ 20y + 25)
A)
64y3+ 100y2– 125
B)
16y3+ 125
C)
D)
64y3– 125
Answer:
D
41
Answer:
B
265)
(9m2+ m – 6)(7m + 2)
A)
63m3– 40m – 12
B)
63m3+ 11m2– 40m – 12
C)
63m3+ 25m2– 40m – 12
D)
16m2– 40m – 12
266)
(-9y – 8)(5y2– y – 9)
A)
-45y3– 49y2+ 89y + 72
B)
-45y3+ 89y + 72
C)
14y2+ 89y + 72
D)
-45y3– 31y2+ 89y + 72
D
267)
(5x2– 2x – 5)(x2+ 2x + 3)
A)
5x4+ 10x3+ 6x2– 16x – 15
B)
5x4+ 8x3+ 6x2– 16x – 15
C)
5x4+ 8x3+ 11x2– 16x – 15
D)
5x4+ 10x3+ 11x2– 16x – 15
B
268)
(3r2– 2r+ 5)(r2+ 2r– 1)
A)
3r4+ 4r3– 2r2+ 12r– 5
B)
3r4+ 4r3– 7r2+ 12r– 5
C)
3r4+ 6r3– 7r2+ 12r– 5
D)
3r4+ 6r3– 2r2+ 12r– 5
A
269)
(2s + 5)(4s3– 3s2– 5s+ 2)
A)
8s4+ 14s3– 25s2+ 4s+ 10
B)
8s4– 21s3– 25s2– 21s+ 10
C)
8s4+ 14s3– 35s2– 21s+ 10
D)
8s4+ 14s3– 25s2– 21s+ 10
D
270)
x +1
53x3+2x2–4x –2
A)
3x4+13
5x3+22
5x2+14
5x –2
5
B)
3x4+13
5x3+22
5x2–14
5x –2
5
C)
3x4–13
5x3+ 18
5x2– 14
5x +2
5
D)
3x4+13
5x3– 18
5x2–14
5x –2
5
D
271)
(4x – 10)(x – 10)
A)
x2+ 100x – 50
B)
x2– 50x – 51
C)
D)
4x2– 51x + 100
C
272)
(-1 +2x)(-2 +2x)
A)
4x2– 6x + 2
B)
2x2– 6x – 6
C)
D)
4x2– 7x + 2
A
273)
(-7 + x)(4x + 9)
A)
4x2– 20x – 63
B)
4x2– 63x – 19
C)
D)
4x2– 19x – 63
42
C
274)
(-3x – 4)(x – 12)
A)
-3x2+ 32x + 48
B)
-3x2+ 48x + 32
C)
D)
-3x2+ 32x + 32
275)
(x + 10)(-3x – 12)
A)
-3x2– 44x – 120
B)
-3x2– 120x – 42
C)
D)
-3x2– 42x – 120
D
276)
(5x + 11)(4x – 6)
A)
20x2+ 14x – 66
B)
9x2+ 14x – 66
C)
D)
20x2+ 14x + 14
A
277)
(2x – 2)(2x + 2)
A)
4x2– 4
B)
2x2+ 8x – 4
C)
D)
4x2– 8x – 4
A
278)
(4x + 6)(4x + 6)
A)
16x2+ 36x + 48
B)
4x2+ 47x + 36
C)
D)
16x2+ 48x + 36
D
279)
(3x2–2)(x5–4)
A)
12x7–2x5–12x2+8
B)
3x7–2x5–12x2+8
C)
3x8–2x5–12x2–8
D)
3x10 –2x5+12x2–8
B
280)
(5y5+3y3)(4y5+4y3)
A)
20y10 +32y8+12y9
B)
20y25 +32y15 +12y9
C)
20y10 +32y8+12y3
D)
20y10 +32y8+12y6
D
281)
(x – 3)(x + 3)
A)
x2– 9
B)
x2– 6x – 9
C)
D)
x2– 6
A
282)
(5p – 2)(5p + 2)
A)
25p2– 4
B)
25p2– 20p – 4
C)
D)
p2– 4
A
283)
(3y2– 4)(3y2+ 4)
A)
3y2– 16
B)
9y4– 16
C)
D)
9y2+ 16
B
284)
(5n2+6)(5n2–6)
A)
25n4+36
B)
25n4–36
C)
D)
5n4–36
43
A
285)
(x2+ 0.9)(x2– 0.9)
A)
x4– 0.81
B)
x4+ 0.81
C)
D)
x2– 0.81
286)
(9x2– 7x)(9x2+ 7x)
A)
9x4– 7x2
B)
81x4+ 126x3– 49x2
C)
81x4– 126x3– 49x2
D)
81x4– 49x2
287)
(x9+ 9)(x9– 9)
A)
x18 + 81
B)
x18 – 81
C)
D)
x18 – 18x9– 81
288)
(3 –x6)(3+x6)
A)
9–x36
B)
9+x6
C)
D)
9–x12
289)
x –1
3x +1
3
A)
x2– 9
B)
x2– 9x – 9
C)
D)
x2+ 9x – 9
290)
2x +4
52x –4
5
A)
2x2–16
25
B)
4x2–16
25
C)
D)
4x2+16
25
291)
3
5– 12x43
5+ 12x4
A)
9
25 +144x16
B)
9
25 –144x4
C)
D)
9
25 –144x8
292)
(7.1 –x3)(7.1 +x3)
A)
50.41 –x9
B)
50.41 –x6
C)
D)
50.41 +x6
293)
(n + 16)2
A)
n2+ 256
B)
n2+ 32n + 256
C)
D)
n +256
44
294)
(w – 16)2
A)
256w2– 32w + 256
B)
w2– 32w + 256
C)
D)
w +256
295)
(3m + 2)2
A)
3m2+ 4
B)
9m2+ 4
C)
D)
3m2+ 12m + 4
296)
(0.1x + 0.5)2
A)
0.01x2– 0.10x + 0.25
B)
0.01x2+ 0.25
C)
0.01x2– 0.10x – 0.25
D)
0.01x2+ 0.10x + 0.25
297)
(5a – 12)2
A)
5a2– 120a + 144
B)
25a2+ 144
C)
D)
25a2– 120a + 144
298)
(-9 x – 8 )2
A)
81 x2+ 64
B)
-9 x2+ 144 x + 64
C)
D)
-9 x2+ 64
299)
(x2+ 5)2
A)
x4+25
B)
x4+ 5x +25
C)
D)
x4+ 10x2+25
300)
(3 + 2x5)2
A)
4x10 + 12x5+9
B)
4x10 + 6x5+9
C)
D)
4x10 +9
301)
s –
4
7
2
A)
s2–8
7s +16
49
B)
s2–8s +16
C)
D)
s2–8
49 s +16
49
302)
c +
2
9
2
A)
c2+4
9c +4
81
B)
2c +4
9c +4
9
C)
D)
c2+4
9
Multiply mentally.
303)
(x – 16x3)2
A)
x2– 32x4+ 256x6
B)
x2– 32x3+ 256x6
C)
D)
x2– 32x6+ 256x9
304)
3x2–2
53x2+2
5
A)
9x4–4
25
B)
9x2 – 20x –4
25
C)
D)
9x2–4
25
305)
(–a2– 5)2
A)
a4+ 25
B)
a4+ 10a2+ 25
C)
D)
–a4+ 10a2+ 25
Answer:
B
306)
(-5 + 4x)(5+ 4x)
A)
x2– 25
B)
16x2– 40x – 25
C)
D)
16x2– 25
Answer:
D
307)
2x2(4x3+4x2–2x)
A)
8x5+8x4–4x3
B)
8x5+8x4–4x2
C)
D)
8x4+8x3–4x2
Answer:
A
308)
(6x5– 4)2
A)
36x10 – 48x5+16
B)
36x10 – 24x5+16
C)
D)
36x10 +16
Answer:
A
309)
(2x2+ 7)(x + 6)
A)
2x3+ 19x + 42
B)
2x2+ 18x + 42
C)
2x3+ 12x2+ 7x + 42
D)
2x2+ 19x + 42
Answer:
C
310)
(2x2+ 3)(x2+ 11)
A)
2x2+ 24x + 33
B)
2x3+ 22x2+ 3x + 33
C)
2x4+ 25x2+ 33
D)
2x2+ 25x + 33
Answer:
C
311)
(s –4)(s2+2s +4)
A)
s3– 2s2+12s – 16
B)
s3– 2s2– 4s + 16
C)
D)
s3– 2s2– 4s – 16
Answer:
D
312)
(6p – 1)(36p2+ 6p + 1)
A)
36p3– 1
B)
216p3+ 1
C)
D)
216p3– 1
Answer:
D
313)
(t + 6)(t2– 6t + 36)
A)
t3– 36t2– 216
B)
t3– 216
C)
D)
t3+ 36t2+ 216
Answer:
C
46
Answer:
A
Compute each expression and compare.
314)
52+82; (5 +8)2
A)
89; 169; square of sum is greater than sum of squares
B)
89; 26; sum of squares is greater than square of sum
C)
26; 26; both are equal
D)
26; 169; square of sum is greater than sum of squares
315)
42–12; (4 –1)2
A)
15; 9; difference of squares is greater than square of difference
B)
6; 6; both are equal
C)
6; 9; square of difference is greater than difference of squares
D)
15; 6; difference of squares is greater than square of difference
Find the total area of all shaded rectangles.
316)
8
x
x 4
A)
x2+8x +32
B)
x2+32
C)
D)
x2+12
317)
4x 8
4x
8
A)
4x2+64x +64
B)
16x2+32x +64
C)
D)
16x2+64x +64
Evaluate the polynomial.
318)
x2+ 2y2– 3xy for x =4 and y =6
A)
16
B)
160
C)
D)
88
319)
2x2–y2+ 2xy for x =-2 and y =-4
A)
40
B)
-24
C)
D)
-40
320)
–2x2–y2+ xy for x =-1 and y =5
A)
22
B)
-22
C)
D)
18
321)
x2+ 3y2+ 2xy for x =5 and y =2
A)
37
B)
45
C)
D)
67
322)
x2– 4y2– xy for x =2 and y =-3
A)
34
B)
-26
C)
D)
46
323)
x2yz + x + y for x =1, y=-4, and z =1
A)
4
B)
7
C)
D)
-4
324)
yz + xy – z for x =1, y=4, and z =3
A)
19
B)
16
C)
D)
13
48
325)
2x2y – xz3 for x =-3, y=2, and z =3
A)
153
B)
36
C)
D)
117
326)
x2+y2–z2 for x =2, y=4, and z =1
A)
21
B)
16
C)
D)
19
327)
–xyz for x =1, y =-1, and z =3
A)
1
B)
3
C)
D)
81
Solve the problem.
328)
The polynomial 0.041h – 0.018A – 2.69 can be used to estimate the lung capacity, in liters, of a female with
height h cm and age A years. Find the lung capacity of a 65–year–old woman who is 163 cm tall. Round to the
nearest liter.
A)
-3 liters
B)
52 liters
C)
D)
11 liters
329)
An object’s altitude, in meters, is given by the polynomial h + vt – 4.9t2, where h is the height in meters from
which the launch occurs, v is the initial upward speed in meters per second, and t is the number of seconds for
which the rocket is airborne. A pebble is shot upward from the top of a building 107 meters tall. If the initial
speed is 39 meters per second, how high above the ground will the pebble be after 2 seconds? Round results to
the nearest tenth of a meter.
A)
165.4 meters
B)
204.6 meters
C)
D)
233.4 meters
330)
A pipette has the shape of a right circular cylinder with a right circular cone at its end. The pipette is used to
inject a nutritive suspension into a colony of microbes. The volume, in cubic centimeters, of a pipette of height h
and radius r, both in centimeters, is given by the polynomial 1
3r2h +r2h. How much nutritive suspension
can be provided if the pipette has a radius of 0.4 cm and a height of 4.7 cm? Use 3.14 for and round to the
nearest tenth cubic centimeter.
A)
1.6 cm3
B)
37 cm3
C)
D)
3.1 cm3
331)
An oval running track encircles a soccer field that is x yards wide and y yards long (see figure). The area A of
the region enclosed by the track can be calculated using the equation A = xy +x
2
2. Calculate the area if
x =78 yd and y =118 yd. Use the approximation
3.14.
A)
9326 yd2
B)
28,308 yd2
C)
D)
13,980 yd2
332)
Liquid propane fuel is frequently stored in tanks that are shaped like the one shown in the figure below. The
volume V of the tank can be computed using the formula V =4
3x
2
3
+yx
2
2. If x =2.3 ft and y =4.7 ft,
calculate the volume of the tank. Use the approximation
3.14.
A)
26 ft3
B)
45 ft3
C)
D)
13 ft3
Give the coefficient and degree of the term.
333)
–12z
A)
12, 0
B)
12, 1
C)
D)
–12, 1
334)
–5y12
A)
12, 5
B)
–5, 12
C)
D)
12, -5
335)
–11x11y13
A)
11, 24
B)
11, 143
C)
D)
–11, 24
336)
4x4y3z4
A)
4, 12
B)
4, 11
C)
4, 4
D)
4, degree undefined
Find the degree of the polynomial.
337)
x6+y4– 3x4y
A)
7
B)
15
C)
D)
4
Answer:
C
338)
x2y –x4+ 5xy –7
A)
3
B)
2
C)
D)
7
Answer:
C
339)
–y5+ 4x5+ 2x5y +3
A)
6
B)
3
C)
D)
5
Answer:
A
340)
2x5+ 4x3+ 2x2–1
A)
2
B)
3
C)
D)
4
Answer:
C
341)
8+x7–x5y4–x4y
A)
9
B)
4
C)
D)
7
Answer:
A
342)
14x8yz –6x6y2+x5yz3
A)
6
B)
8
C)
D)
10
Answer:
D
343)
x5yz –x7y2–4x4y2z3
A)
4
B)
7
C)
D)
9
Answer:
D
344)
z6y +3–x6+z5x3
A)
6
B)
7
C)
D)
8
Answer:
D
345)
xyz5+x5y4+ xz4
A)
7
B)
5
C)
D)
4
Answer:
C
346)
–7y5–3x4z +7xz4
A)
5
B)
4
C)
D)
3
Answer:
A
51
Answer:
B
Collect like terms.
347)
-9y – 6x – 3x
A)
-18xy
B)
-9y – 9x
C)
D)
-9y – 3x
348)
-12n3– 11n3
A)
-23n6
B)
132n3
C)
D)
-23n3
D
349)
-6q3– 11q3+ 3q3
A)
198q3
B)
198q9
C)
D)
-14q3
D
350)
2y3– 12y– 9y3– 7
A)
216y3– 7
B)
-19y3– 7
C)
D)
-26y3
C
351)
p3+ 9p4+ 3p2–p4+ 7p3
A)
9p4– 8p3+ 3p2
B)
-8p4– 8p3 – 3p2
C)
D)
8p4+ 8p3+ 3p2
D
352)
5x2y + 9z2y + 6x2y + 9z2y
A)
29x2y
B)
11x2y + 18z2y
C)
D)
29z2y
B
Add.
353)
(12s +10t) + (2t –5s)
A)
17s +12t
B)
19st
C)
D)
14s +5
C
354)
(r + 4s + 3) + (-3r + s) + (s + 2)
A)
-2r + 5s + 5
B)
-3r + 4s + 5
C)
D)
-4r + 6s + 5
C
355)
(x3y2+ 5x2y3+ 3xy + 4) + (x2y3+ 7x3y2+ 5xy – 3)
A)
2x3y2+ 12x2y3+ 8xy + 1
B)
8x3y2+ 6x2y3+ 8xy + 1
C)
8x3y2+ 6x2y3+ 3xy + 1
D)
6x3y2+ 6x2y3+ 8xy + 1
B
356)
(4x2– 2xy +y2) + (-2x2+ 5xy –y2) + (x2+ xy –y2)
A)
3x2+ 4xy –y2
B)
3x2+ 4xy +y2
C)
D)
1x2+ 2xy –y2
A
52
B
Subtract.
357)
(30x +7xy –8y) – (6x –10xy –18y)
A)
51xy
B)
23x – 24xy +26
C)
D)
24x –17xy –26y
358)
(2x2y + 2xy) – (5x2y – 10xy2+ 5xy)
A)
-3x2y + 10xy2+ 7xy
B)
-3x2y – 10xy2– 3xy
C)
-3x2y + 10xy2– 3xy
D)
-8x2y – 5xy2– 3xy
C
359)
(-4a – 2b – c) – (7b – 4c – 4d)
A)
-4a – 9b + 5c + 4d
B)
-4a – 9b + 3c + 4d
C)
D)
-4a – 9b + 3c – 4d
B
Multiply.
360)
(p + 3q)(p – 3q)
A)
p2– 6pq – 9q2
B)
p2+ 6pq – 9q2
C)
D)
p2– 9q2
D
361)
(8y + x)(8y – x)
A)
64y2+ 16xy – x2
B)
64y2– x2
C)
D)
64y2– 16xy – x2
B
362)
(3a + 10c)(3a – 10c)
A)
9a2– 60ac – 100c2
B)
9a2– 100c2
C)
D)
9a2+ 60ac – 100c2
B
363)
(11m – 8w)(11m + 8w)
A)
11m2– 8w2
B)
121m2+ 176mw – 64w2
C)
121m2– 176mw – 64w2
D)
121m2– 64w2
D
364)
(5x + 7y)2
A)
5x2+ 70xy + 49y2
B)
5x2+ 49y2
C)
D)
25x2+ 49y2
C
365)
(9x – 7y)2
A)
81x2+ 49y2
B)
81x2– 126xy + 49y2
C)
9x2– 126xy + 49y2
D)
9x2+ 49y2
B
366)
(w – z)(w2+z2+3wz)
A)
w3+3 wz2–3w2z –z3
B)
w3+2wz2–2w2z –z3
C)
w3–3 wz2+3w2z –z3
D)
w3–2wz2+2w2z –z3
D
53
C
367)
(x2+6y2– xy)(x2+3xy +y2)
A)
x4+2x3y + 4x2y2+19xy3–6y4
B)
x4+2x3y + 4x2y2+17xy3+6y4
C)
x4+4x3y + 4x2y2+17xy3–6y4
D)
x4+4x3y +10x2y2+17xy3+6y4
368)
(x + y – 2)(x + y + 2)
A)
x2+y2–4
B)
x2+y2+ 2(xy –2)
C)
D)
x2+y2+ 2xy –4
369)
(a – b)(a2– ab –9b2)
A)
a3– 2a2b –9ab2+9b3
B)
a3–8a2b +9b3
C)
a3– 2a2b –8ab2+9b3
D)
a3– 2a2b –10ab2–9b3
Divide.
370)
12x6+ 54x
6
A)
2x6+ 54x
B)
2x5+ 9
C)
D)
2x6+ 9x
371)
6x8– 9x5+ x2
x
A)
6x7– 9x5+ x2
B)
6x7– 9x4+ x
C)
D)
-3
372)
20x7+ 10x2– 20x
2x
A)
10x7+ 5x2– 10x
B)
10x7+ 10x2– 20x
C)
D)
10x6+ 5x – 10
373)
(10x8+ 10x6+ 4x3) ÷ (-1x3)
A)
10x5+ 10x3+ 4
B)
-10x5+ 10x6+ 4x3
C)
D)
-10x5– 10x3– 4
374)
56x2– 32x – 1
8
A)
7x2– 32x – 1
B)
56x2– 32x – 1
C)
D)
7x – 4 – 1
8
375)
9x4 – 2x3+ 5x2
x2
A)
9x4– 2x3+ 5
B)
9x4– 2x + 5x2
C)
D)
9
2x4– 1x3+ 5
2
376)
8x8– 16x6
2x4
A)
4x4– 16x6
B)
-4x10
C)
D)
4x4– 8x2
377)
-8x8– 40x5÷-4x2
A)
-8x8+ 10x3
B)
2x6– 40x5
C)
D)
2x6+ 10x3
378)
36w5
6w4
A)
w9
6
B)
1
6
C)
D)
6w
379)
8x3y4+12x5y8–12x6y5
4x3y4
A)
2xy +3x2y4–3x3y
B)
2+3xy4–3x2y
C)
2+3x2y3–3x3y2
D)
2+3x2y4–3x3y
Perform the division.
380)
(x2– 16) ÷ (x + 4)
A)
x – 4
B)
x – 16
C)
D)
x + 16
381)
(x2– 121) ÷ (x – 11)
A)
x2– 11
B)
x + 121
C)
D)
x – 121
382)
x3+ 27
x + 3
A)
x2– 6x + 9
B)
x2– 3x + 9
C)
D)
x2– 3x – 9
383)
z3– 8
z – 2
A)
z2+ 2z – 4
B)
z2+ 4z + 4
C)
D)
z2+ 2z + 4
384)
x4– 625
x2– 25
A)
x2+ 5x + 5
B)
x2+ 25
C)
D)
x2– 25
385)
(x4– 16) ÷ (x + 2)
A)
x3+ 2x2+ 4x + 8
B)
x2+ 2x + 4
C)
D)
x3– 2x2+ 4x – 8
386)
x4+ 3x2+ 5
x2+ 1
A)
x2+ 2 +1
B)
x2+ 2
C)
D)
x2+ 2 +3
x2+ 1
387)
x4– 1
x2– 1
A)
x2
B)
x2– 1
C)
D)
x2+ 1
388)
-25x3– 30x2– 18x – 4
5x + 2
A)
–5x2– 2
B)
–5x2– 4x – 2
C)
D)
x2– 4x – 2
389)
15x3– 19x2– 14x + 31
-5x + 3
A)
-3x2+ 2x + 4 +22
-5x + 3
B)
-3x2+ 2x + 4 +19
-5x + 3
C)
x2+ 4 +2
-5x + 3
D)
-3x2+ 2x + 4
Provide an appropriate response.
390)
True or false? r
s
5
=
r5
s
A)
True
B)
False
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
391)
Simplify the expressions (2x)0 and (2x0) and explain how you arrived at your answers.
392)
When is the square of the sum the sum of a square; i.e., when is (A + B)2=A2+B2 ?
393)
What must be done to the dividend before beginning the “long division” process for
(6y2+ 2y4+ 7y3+ 2y+ 2) ÷ (3y + 5)?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
394)
Rank the numbers in order from smallest to largest.
2.46 x 10 3, 3.68 x 10 5, 3.18 x 10 -5 , 3.14 x 10 3, 4.68 x 10 -6
A)
3.68 x 10 5<3.14 x 10 3<2.46 x 10 3<3.18 x 10 -5 <
4.68 x 10 -6
B)
3.18 x 10 -5 <4.68 x 10 -6 <2.46 x 10 3<3.14 x 10 3<
3.68 x 10 5
C)
4.68 x 10 -6 <3.18 x 10 -5 <2.46 x 10 3<3.14 x 10 3<
3.68 x 10 5
D)
4.68 x 10 -6 <2.46 x 10 3<3.14 x 10 3<3.68 x 10 5<
3.18 x 10 -5
395)
Tell whether or not the number is given in scientific notation.
6.542 x 10 3
A)
Yes
B)
No
396)
Tell whether or not the number is given in scientific notation.
63.87 x 10 -10
A)
Yes
B)
No