143)
The height H (in feet) of a ball thrown into the air from the top of a building after t seconds is given by
H = – 16t2+62t +209. Use the graph below to estimate the height of the ball after 2.5 seconds.
A)
220 feet
B)
300 feet
C)
260 feet
D)
360 feet
144)
The height H (in feet) of a ball thrown into the air from the top of a building after t seconds is given by
H = – 16t2+47t +227. Use the graph below to find the approximate value of –16t2+47t +227 for x =1.
A)
358 feet
B)
298 feet
C)
218 feet
D)
258 feet
145)
Participants in a memorization experiment were able to recall an average of D digits in t minutes, where
D =-0.4t2+9t. Use the graph below to estimate the number of digits recalled after 5 minutes.
A)
75 digits
B)
35 digits
C)
15 digits
D)
55 digits
146)
Participants in a memorization experiment were able to recall an average of D digits in t minutes, where
D =-0.2t2+9t. Use the graph below to find the approximate value of -0.2t2+9t for t =2.
A)
37 digits
B)
-3 digits
C)
57 digits
D)
17 digits
Identify the terms in the polynomial.
147)
3x4–4x2–3x –4
A)
3x4, 4x2, 3x, 4
B)
3x4, -4x2, -3x, -4
C)
3, x4, -4, x2, -3, x, -4
D)
3, x4, 4, x2, 3, x, 4
148)
4y11 –11y2–4y
A)
4y11, 11y2, -4y
B)
4y11, -11y2, 4y
C)
4, y11, -11, y2, -4, y
D)
4y11, -11y2, -4y
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
149)
-2x2
A)
Binomial, degree -2
B)
Monomial, degree 2
C)
Binomial, degree 0
D)
Monomial, degree -2
Answer:
B
150)
-12x
A)
Monomial, degree -12
B)
Monomial, degree 0
C)
Monomial, degree 1
D)
Binomial, degree 0
Answer:
C
151)
16a8
A)
Monomial, degree 16
B)
Binomial, degree 8
C)
Monomial, degree 8
D)
Binomial, degree 16
Answer:
C
152)
5y8– 5
A)
Monomial, degree 5
B)
Binomial, degree 8
C)
Binomial, degree 9
D)
Binomial, degree 0
Answer:
B
153)
-5z + 6
A)
Binomial, degree 2
B)
Binomial, degree 1
C)
Monomial, degree -5
D)
Binomial, degree 0
Answer:
B
154)
11s4– 3s – 6
A)
Trinomial, degree 6
B)
Trinomial, degree 5
C)
Trinomial, degree 4
D)
Binomial, degree 5
Answer:
C
155)
6y5+ 2y4+ 2
A)
Trinomial, degree 9
B)
Trinomial, degree 10
C)
Binomial, degree 5
D)
Trinomial, degree 5
Answer:
D
156)
19c6– 8c5– 7c4
A)
Binomial, degree 5
B)
Trinomial, degree 15
C)
Trinomial, degree 6
D)
Binomial, degree 15
Answer:
C
Answer:
D
157)
-5z4+ 3z3+ 6z2+9
A)
Trinomial, degree 4
B)
None, degree 4
C)
Binomial, degree 10
D)
Trinomial, degree 9
158)
-9x3+ 3w2– 7w – 5w4– 2
A)
Trinomial, degree 4
B)
None, degree 4
C)
Binomial, degree 11
D)
Trinomial, degree 10
Identify the coefficient of each term of the polynomial.
159)
-6a
A)
-6a
B)
-6
C)
6a
D)
6
160)
-2a+ 5a2
A)
2 and 5
B)
2
C)
-2 and 5
D)
-2
161)
-6h– 4m
A)
-6 and 4
B)
6 and -4
C)
-6 and -4
D)
6 and 4
162)
-5z– 3y
A)
-5 and 3
B)
5 and 3
C)
5 and -3
D)
-5 and -3
163)
7b– 3x– z
A)
7, 3, 1
B)
7 and -3
C)
7, -3, 1
D)
7, -3, –1
164)
-9b– 7m– s
A)
9, 7, –1
B)
9, -7, 1
C)
-9, -7, –1
D)
-9, 7, 1
Identify the degree of each term and the degree of the polynomial.
165)
4x –7
A)
4, -7; 7
B)
4, 0; 4
C)
1, 0; 1
D)
1, -7; 1
166)
7x2–9x +7
A)
2, 1, 0; 2
B)
2, 0, 0; 2
C)
2, 1, 0; 7
D)
7, -9, 7; 7
167)
2x –2x2+3–4x3
A)
1, –2, 0, –3; 1
B)
2, -2, 3, -4; 2
C)
3, 2, 1, 0; 3
D)
1, 2, 0, 3; 3
24
168)
3x5–3x2+3–5x3
A)
3, -3, 3, -5; 3
B)
5, 3, 2, 0; 5
C)
5, –2, 1, –3; 5
D)
5, 2, 0, 3; 5
Identify the like terms in the polynomial.
169)
4x3+6x2–8x3
A)
x3
B)
4x3 and -8x3
C)
4x3 and 8x3
D)
None of the terms are like.
170)
5z4–4z5–3z3+5z5+6z4+9
A)
z5, z4, z3, and 9
B)
-4z5 and 5z5; 5z4 and 6z4
C)
-4z5 and 5z5; 5z4 and 6z4; -3z3 and 9
D)
None of the terms are like.
Collect like terms.
171)
4x3+ 6x3
A)
10x6
B)
10x3
C)
Can’t be simplified
D)
30x
172)
9x7+ 3x7+14
A)
84x +14
B)
12x7+14
C)
12x14 +14
D)
Can’t be simplified
173)
6x8+ 9x8– 3x8
A)
–162x8
B)
12x24
C)
12x8
D)
Can’t be simplified
174)
6x8+ 9x3+ 4x8
A)
10x8+ 9x3
B)
19x3
C)
Can’t be simplified
D)
19x19
175)
5a3– 12a3+ 15a2+ 2a3– 14a2
A)
Can’t be simplified
B)
–5a3+ 1a2
C)
–4a5
D)
–4a3
176)
–3b7+ 14b6– 2b2+ 11b7– 13b6
A)
135b
B)
9b15
C)
Can’t be simplified
D)
8b7+ 1b6– 2b2
25
177)
3x8–1
2x+ 9x4+1
4x + 7x8
A)
19x20 –1
4x
B)
19x4+1
4x
C)
10x8+ 9x4–1
4x
D)
10x8+ 9x4+1
4x
178)
1
4x3– x +10 +4
5x3+9x –6
A)
6
13 x3+8x +4
B)
21
20 x3+8x +16
C)
21
20 x3+8x +4
D)
21
20 x3+10x+4
Arrange the polynomial in descending order.
179)
-9 – 7x2+ 6x6– 3x3+ x
A)
-9 + x – 7x2– 3x3+ 6x6
B)
6x6+ x – 3x3– 7x2– 9
C)
-9 – 7x2+ 6x6– 3x3+ x
D)
6x6– 3x3– 7x2+ x – 9
180)
x6+ x +9x3+2+4x2
A)
2+ x +4x2+9x3+x6
B)
x +4x2+9x3+x6+2
C)
x6+9x3+4x2+ x +2
D)
9x3+4x2+2+x6+ x
181)
-10 + 8p2+ 6p9– 3p3– 2p
A)
-10 – 2p + 8p2– 3p3+ 6p9
B)
8p2– 2p – 3p3+ 6p9– 10
C)
6p9– 3p3+ 8p2– 2p – 10
D)
-10 + 8p2+ 6p9– 3p3– 2p
Collect like terms and then arrange in descending order.
182)
4x4– 3x5+6x4– 5x5
A)
2x18
B)
10x10 – 8x8
C)
-8x5+10x4
D)
2x9
183)
-2x4+ 5x6– 7x +5x6– 8x – 6x4
A)
–3x6+ 3x4– 13x
B)
10x6– 8x4– 15x
C)
10x – 8x6– 15x4
D)
-13x11
184)
8+ 4x6+ 2x5+8x6+ 2x5– 7
A)
16x6+ 6x5– 5
B)
12 + 4x6+ 1x5
C)
17x11
D)
12x6+ 4x5+ 1
185)
12x4+ 13x5– 7x4+4x5– 15x5
A)
7x9
B)
7x5
C)
2x5+ 5x4
D)
Can’t be simplified
26
186)
–9x9– 15x2+ 5x7+ 4x9– 12x7
A)
-5x9– 7x7– 15x2
B)
17x18
C)
Can’t be simplified
D)
306x
187)
8x2+ 7x4+ 3x3– 3x2+3x3+ 3x4
A)
10x8+ 6x6+ 5x4
B)
21x18
C)
10x4+ 6x3+ 5x2
D)
6x4+ 6x3+ 10x2
188)
–3+5x +6
5x3+4– x +1
4x3
A)
29
20 x3+4x +1
B)
7
9x3+4x +1
C)
29
20 x3+4x +7
D)
29
20 x3+6x +1
Identify the missing terms in the polynomial.
189)
x3–9
A)
x2–term, x–term
B)
x2–term
C)
x4–term, x2–term, x–term
D)
x–term
190)
-3x3
A)
none
B)
x–term
C)
x2–term, x–term, 0–degree term
D)
x2–term, x–term
191)
5x3–5x2+ x +5
A)
None
B)
x4–term
C)
x4–term, x2–term, x–term
D)
x–term
192)
3x2–16
A)
x3–term
B)
None
C)
x2–term
D)
x–term
Write the polynomial in two ways: with its missing terms and by leaving space for them.
193)
w3+8
A)
w3+0w2+8
w3+8
B)
w3+0w2+0w +8
w3+8
C)
w3+0w +8
w3+8
D)
w3+8
w3+8
27
194)
2x4–5x2+8x
A)
2x4+0x3+5x2+8x +0
2x4+5x2+8x
B)
2x4–5x2+8x +0
2x4–5x2+8x
C)
2x4+0x3–5x2+8x
2x4–5x2+8x
D)
2x4+0x3–5x2+8x +0
2x4–5x2+8x
195)
–8x2
A)
–8x2+ 0x0
–8x2
B)
–8x2+ 0x
–8x2
C)
–8x2+ 0x + 0x0
–8x2
D)
None missing
C
Add.
196)
(8x – 3) + (7x – 8)
A)
4x
B)
56x + 24
C)
15x – 11
D)
56x – 11
C
197)
(7 + 8x7+ 5x4) + (9x7+ 4x4+ 9)
A)
16x7+ 12x4+ 14
B)
17 + 9x7+ 16x4
C)
42x11
D)
17x7+ 9x4+ 16
D
198)
(6– 8x5+ 3x7– 7x6) + (-9x6– 2x5– 8 + 4x7)
A)
7x14 – 16x12 – 10x10 – 2
B)
-3x7– 3x6– 5x5– 3
C)
7x7– 16x6– 10x5– 2
D)
-19x36 – 2
C
199)
(2x8–6x4+5x2+4) + (2x7+4x4–3x)
A)
2x8+ 2x7– 2x4+ 5x2– 3x + 4
B)
4x8– 2x4+ 5x2– 3x + 4
C)
4x8– 10x4+ 5x2– 3x + 4
D)
2x8+ 2x7+ 2x4+ 5x2– 3x + 4
A
200)
9x5– 9x4
4x5+ 5x4
A)
13x5– 4x4
B)
9x18
C)
13x10 – 4x8
D)
9x9
A
201)
4x6+ 2x4+ 8
5x6– 9x4+ 2
A)
13x6– 5x4+ 4
B)
12x10
C)
9x6– 7x4+ 10
D)
9– 7x6+ 10x4
C
28
D
202)
3x5+ 9x4– 2x3+ 1
2x5+ 9x4+ 6x3+ 4
A)
10x5+ 10x4+ 7x3+ 11
B)
27x24 + 5
C)
5x5+ 18x4+ 4x3+ 5
D)
5x10 + 18x8+ 4x6+ 5
203)
1
3x2– 5
8x + 3
5
1
6x2– 3
4x + 3
10
A)
1
6x2+ 11
8x + 9
10
B)
1
6x2– 11
8x + 9
10
C)
1
2x2+ 11
8x + 9
10
D)
1
2x2– 11
8x + 9
10
204)
0.25x4–1.45x3–x2+0.08x –0.8
0.49x4+0.48x2–1.03
0.04x3–0.67x+0.87
0.74x4–x3+0.88x
A)
1.48x4– 1.41x3+ 0.48x2+ 0.29x – 0.96
B)
1.48x12 – 2.41x9– 0.52x4+ 0.29x – 0.96
C)
1.48x4– 2.41x3– 0.52x2+ 0.29x – 0.96
D)
1.48x4– 2.49x3– 0.52x2+ 1.63x – 0.96
Simplify.
205)
–(–5x)
A)
0
B)
1
5x
C)
–5x
D)
5x
206)
–(5x –8)
A)
5x –8
B)
–5x –8
C)
–5x +8
D)
5x +8
207)
–(2x2–6x +8)
A)
2x2+6x –8
B)
–2x2+6x –8
C)
–2x2–6x –8
D)
2x2–6x +8
29
208)
–(–5x4+7x2+5
7x –3)
A)
–5x4+7x2+5
7x –3
B)
5x4+7x2–5
7x +3
C)
5x4+7x2+5
7x –3
D)
5x4–7x2–5
7x +3
209)
–(–6x4–4x3–x2+7.3)
A)
6x4–4x3+x2–7.3
B)
–6x4–4x3–x2+7.3
C)
6x4–4x3–x2+7.3
D)
6x4+4x3+x2–7.3
D
Subtract.
210)
(–16x + 4) – (5x + 2)
A)
–21x + 2
B)
-11x + 6
C)
-19x
D)
–21x + 6
A
211)
(4x5+ 20x2+ 18) – (-2x2+ 7x5+ 14)
A)
–3x5+ 27x2+ 32
B)
23x7
C)
–3x5+ 22x2+ 4
D)
–3x5+ 22x2+ 32
C
212)
(8x + 4x6+ 4x5) – (9x5+ 7x6+ 15x)
A)
-3x6+ 11x5+ 23x
B)
-15x12
C)
-3x6– 5x5– 7x
D)
-3x6– 5x5+ 23x
C
213)
(-4x6+ 6x8– 6 – 5x7) – (-9 + 9x7+ 8x8+ 6x6)
A)
-2x8+ 4x7+ 2x6– 15
B)
-2x8– 14x7– 10x6+ 3
C)
14x8+ 4x7+ 2x6+ 3
D)
14x8+ 4x7+ 2x6– 15
B
214)
(-4x7+ 2x9+ 9 + 9x8) – (5– 3x8+ 8x9+ 7x7)
A)
10x9+ 6x8+ 3x7+ 14
B)
-6x9+ 6x8+ 3x7+ 14
C)
-6x9+ 12x8– 11x7+ 4
D)
10x9+ 6x8+ 3x7+ 4
C
215)
2x4– 7x2
–(8x4+ 9x2)
A)
10x4+ 2x2
B)
-6x4+ 2x2
C)
-22x6
D)
-6x4– 16x2
D
D
216)
3x5– 15x3+ 8
–( 9x5– 12x3– 19)
A)
-6x5– 3x3– 11
B)
-6x5– 3x3+ 27
C)
-6x5– 6x3– 11
D)
18x8
217)
9x7+ 7x6– 3x5– 2
–(3x7+ 3x6+ 5x5– 3)
A)
6x7+ 10x6+ 2x5– 5
B)
12x7+ 10x6+ 2x5– 5
C)
12x7+ 10x6+ 2x5+ 1
D)
6x7+ 4x6– 8x5+ 1
218)
(0.5x4–0.8x2+0.5) – (3.9x4+1.5x –3.7)
A)
-3.4x4– 0.8x2– 1.5x + 4.2
B)
-3.4x4– 0.5x2– 3.2
C)
-3.4x4– 0.8x2+ 1.5x + 4.2
D)
-3.4x4– 0.8x2– 1.5x – 3.2
219)
9x4+ 8x3+ 1
–(x4– 6x3+x2– 9x )
A)
8x4+14x3+x2–9x +1
B)
8x4+2x3–x2–9x +1
C)
8x4+14x3+x2–8x
D)
8x4+14x3–x2+9x +1
Solve the problem.
220)
Find a polynomial for the sum of the areas of these rectangles.
x x
x 5
A)
x2+5x + 1
B)
x2+5x
C)
6x2
D)
6x
221)
Find a polynomial for the sum of the areas of these circles.
r14 8
A)
(260 +)r2
B)
r2+196
C)
+260
D)
r2+260
222)
Find a polynomial for the perimeter of the figure.
2z 2
2z 2z
6
7z 7z
6
2z 2z
2z 2
A)
42z
B)
26z +8
C)
22z +16
D)
26z +16
223)
Find a polynomial for the perimeter of the figure.
8a
4a
3a
a
9a 4a 2a
5
3
4a
A)
43a
B)
35a +8
C)
43
D)
35a +10
224)
Find a polynomial for the sum of the shaded areas of the figure.
y 7
y
7
A)
y2+14y +49
B)
50y2
C)
50
D)
y2+49
225)
Find a polynomial for the sum of the shaded areas of the figure.
z 3
z
3
A)
6
B)
z2+6z +9
C)
6z
D)
z2+9
226)
Find a polynomial for the sum of the shaded areas of the figure.
r
6
4
A)
r2–36
B)
r2–20
C)
r2+16
D)
r2+20
227)
Find a polynomial for the sum of the shaded areas of the figure.
n
n
5
6
A)
n2
B)
n2+30
C)
n2–30
D)
n2+ 2n +30
228)
Find a polynomial for the the shaded areas of the figure.
r
r
A)
(4 –)r2
B)
( – 4)r2
C)
r2
D)
( – 1)r2
229)
Find a polynomial for the the shaded areas of the figure.
4
x x
x x
4
x x
x x
A)
4x2–16x +16
B)
4x2–16x
C)
4x2
D)
8x2–16x +16
Multiply.
230)
(5m2)(2m3)
A)
–10m5
B)
–10m
C)
10m5
D)
10m
C
231)
2(3x)
A)
5
B)
5x
C)
6
D)
6x
D
232)
(–6x3)(9x2)
A)
15x5
B)
–54x5
C)
–54x6
D)
15x6
B
233)
(-0.1x2)(0.9x5)
A)
–0.09x7
B)
0.09x10
C)
0.09x7
D)
–0.09x10
A
234)
1
4x2– 1
7x6
A)
1
28 x8
B)
– 1
28 x12
C)
– 1
11 x12
D)
– 1
28 x8
D
D
235)
(-7x5)(3x4)(2x2)
A)
42x40
B)
42x11
C)
-42x11
D)
-42x40
236)
(5x2)(0)
A)
5
B)
0
C)
5x2
D)
1
237)
(–5x3)(–1)
A)
1
B)
5
C)
–5x3
D)
5x3
238)
-6(6x + 9)
A)
-36x + 9
B)
-90x
C)
6x – 54
D)
-36x – 54
239)
-4x(2x – 1)
A)
2x2+ 4x
B)
-8x2+ 4x
C)
-4x2
D)
-8x2– 1x
240)
-4x5(3x + 8)
A)
–12x – 32
B)
-44x5
C)
–12x6– 32x5
D)
–12x6+ 8
241)
-2x4(5x5– 7)
A)
–10x5+ 14
B)
–10x9– 7
C)
–10x9+ 14x4
D)
4x4
242)
9x5(10x6– 11x2)
A)
90x11 – 99x7
B)
-9x11 – 9x7
C)
-9x5
D)
90x11 – 11x2
243)
11x4(-12x6– 4x3)
A)
-132x2– 44x
B)
-132x10 – 44x7
C)
-132x10 + 44x7
D)
-132x10 – 4x3
244)
-5x6(-8x7+ 12x5– 2)
A)
40x13 + 12x5– 2
B)
40x7– 60x5+ 10
C)
40x13 – 60x11 + 10x6
D)
40x13 – 60x11
245)
10x7(-6x3– 10x2+ 8)
A)
-60x10 – 10x2+ 8
B)
-60x3– 100x2+ 80
C)
-60x10 – 100x9+ 80x7
D)
-60x10 – 100x9
37
246)
-2x8(-9x5+ 12x4+ 7)
A)
18x13 + 12x4+ 7
B)
18x13 – 24x12 – 14x8
C)
18x13 – 24x12 + 7
D)
18x5– 24x4– 14
247)
(x + 12)(x + 11)
A)
x2+ 20x + 132
B)
x + 23x + 132
C)
x2+ 23x + 132
D)
x2+ 23x + 23
C
248)
(x + 4)(x – 4)
A)
x2+ 8x – 16
B)
x2– 8
C)
x2– 8x – 16
D)
x2– 16
D
249)
(2x + 12)(x + 4)
A)
2x2+ 20x + 48
B)
2x2+ 19x + 48
C)
x2+ 20x + 19
D)
x2+ 48x + 20
A
250)
(-3x – 7)(x – 8)
A)
-3x2+ 17x + 56
B)
-3x2+ 17x + 17
C)
-3x2+ 15x + 56
D)
-3x2+ 56x + 17
A
251)
(5x – 3)(-2x + 12)
A)
3x2+ 66x + 66
B)
-10x2+ 66x – 36
C)
-10x2+ 66x + 66
D)
3x2+ 66x – 36
B
252)
(4x – 10)(4x + 10)
A)
16x2+ 80x – 100
B)
4x2+ 80x – 100
C)
16x2– 100
D)
16x2– 80x – 100
C
253)
(3x + 11)(3x + 11)
A)
3x2+ 65x + 121
B)
9x2+ 66x + 121
C)
9x2+ 121x + 66
D)
3x2+ 66x + 65
B
254)
t +9
2t +9
2
A)
t2+9t +81
4
B)
t2–81
4
C)
t2+9
2t +81
4
D)
t2+81
4
A
255)
(x –0.7)(x +0.7)
A)
x2+0.49
B)
x2–1.4x –0.49
C)
x2–1.4x +0.49
D)
x2–0.49
D
256)
(x – 1.9)(x + 3.3)
A)
x2– 1.4x – 6.27
B)
x2– 5.2x – 6.27
C)
x2+ 1.4x – 6.27
D)
x2+ 5.2x – 6.27
38
B
Write an algebraic expression that represents the total area of the four smaller rectangles.
257)
x 7
x
8
A)
x2+ 14x + 49
B)
x2+ 15x + 56
C)
x2+ 16x + 64
D)
x2– 15x + 56
258)
x 4
x
5
A)
x2– 8x + 16
B)
x2+ 9x + 20
C)
x2+ 8x + 16
D)
x2+ 10x + 25