Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve
the polynomial equation.
203)
4x3+ 23x2+ 31x + 12 = 0; –4
203)
A)
The remainder is zero; –1
4, –3, –4
B)
The remainder is zero; –3
4, 1, –4
C)
The remainder is zero; 3
4, –1, –4
D)
The remainder is zero; –3
4, –1, –4
Use synthetic division and the Remainder Theorem to find the indicated function value.
204)
f(x) =x5– 4x4– 5x3+ 7; f(3)
204)
A)
–17
B)
–209
C)
209
D)
–452
Solve the equation for the specified variable.
205)
1
a+1
b=1
c for c
205)
A)
c = ab(a + b)
B)
c = a + b
C)
c =ab
a + b
D)
c =a + b
ab
Simplify the complex fraction.
206)
5
a+ 1
5
a– 1
206)
A)
5–a2
B)
a2
5–a2
C)
5+ a
5– a
D)
5
If y varies inversely as x, find the inverse variation equation for the situation.
207)
y =18 when x =1
9
207)
A)
y =162x
B)
y =x
2
C)
y =1
2x
D)
y =2
x
Use synthetic division to divide.
208)
(2x2+ 17x + 36) ÷ (x + 4)
208)
A)
–2x – 9
B)
2x + 9
C)
x + 9
D)
9x + 4
Divide.
209)
(x2– 25) ÷ (x – 5)
209)
A)
x + 25
B)
x – 25
C)
x2– 5
D)
x + 5
Solve.
210)
The distance that an object falls when it is dropped is directly proportional to the square of the
amount of time since it was dropped. An object falls 39.2 meters in 2 seconds. Find the distance the
object falls in 4 seconds.
210)
A)
156.8 meters
B)
39.2 meters
C)
8meters
D)
78.4 meters
The rational function f(x) =120x
100 – x models the cost, f(x), in millions of dollars, to remove x% of the trash from American
highways. The graph is shown. Use the equation to solve the problem.
211)
According to the cost model, is it possible to remove 100% of the trash from American highways?
211)
A)
Yes
B)
No
Use synthetic division and the Remainder Theorem to find the indicated function value.
212)
f(x) =x4+ 2x3– 7x2+ 6x + 9; f(–2)
212)
A)
–47
B)
–31
C)
31
D)
62
Perform the indicated operations. Simplify where possible.
213)
x3+ 8
x2– 1
÷x2– 2x + 4
x2– 2x + 1
213)
A)
(x + 2)(x + 1)
(x – 1)
B)
(x – 2)(x – 1)
(x – 1)
C)
(x + 2)(x – 1)
(x + 1)
D)
(x – 2)(x – 1)
(x + 1)
60
214)
x
x2– 16
–6
x2+ 5x + 4
214)
A)
x2– 5x + 24
(x – 4)(x + 4)
B)
x2+ 5x + 24
(x – 4)(x + 4)(x + 1)
C)
x2– 5
(x – 4)(x + 4)(x +1)
D)
x2– 5x + 24
(x – 4)(x + 4)(x + 1)
Simplify the complex fraction.
215)
x–2
x–2– y–2
215)
A)
y2
y2– x2
B)
y2
y2+ x2
C)
y2– x2
y2
D)
y
y2– x2
Divide.
216)
16x10 – 12x9+ 28x7+ 20x5+ 7x4
4x7
216)
A)
4x3– 12x9+ 28x7+ 20x5+ 7x4
B)
16x10 – 3x2+ 7 +5
x2+7
4x3
C)
4x3– 3x2+ 7
D)
4x3– 3x2+ 7 +5
x2+7
4x3
Solve the rational equation.
217)
1
x +7+3
x +4=
–3
x2+11x +28
217)
A)
{–7}
B)
C)
{0}
D)
{4}
Find the variation equation for the variation statement.
218)
c varies directly as a and inversely as b; c=2 when a=18 and b=63
218)
A)
c=a
7b
B)
c=7
ab
C)
c=7ab
D)
c=7a
b
The graph of a rational function, f, is shown in the figure. Use the graph to answer the question.
219)
Is –5 a function value of f?
219)
A)
Yes
B)
No
Perform the indicated operations. Simplify where possible.
220)
x2+ 3x – 10
x2+9x +18
·x2+ x – 6
x2+ 10x + 25
·x +6
x – 2
220)
A)
x +6
x – 5
B)
x – 5
x +6
C)
x +6
x + 2
D)
x – 2
x – 5
62
Simplify the rational expression. If the rational expression cannot be simplified, so state.
221)
y3–216
y –6
221)
A)
y2+6y +36
B)
y2–36
C)
Cannot be simplified
D)
1
y –6
Divide as indicated.
222)
x2–13x +42
6– x ÷ (x +7)
222)
A)
–x –7
x +7
B)
–x +7
x –7
C)
–(x –7)(x +7)
D)
–1
Solve the equation for the specified variable.
223)
F =
–GMm
r2 for G
223)
A)
G=
–Fr2
Mm
B)
G=Fr2
Mm
C)
G=
–FMm
r2
D)
G= – Fr2–Mm
The graph of a rational function, f, is shown in the figure. Use the graph to answer the question.
224)
Find all horizontal asymptotes of the graph.
224)
A)
x = 4, x = – 4
B)
y = 4, y = – 4
C)
y = – 6
D)
x = – 6
Solve the rational equation.
225)
2
t=t
5t – 12
225)
A)
0, 24
9
B)
{0}
C)
{4, 6}
D)
{0, 36}
Find the least common denominator of the rational expressions.
226)
x – 1
x2+10x +9 and 2
x2+ x
226)
A)
x(x + 9)(x + 1)
B)
x + 1
C)
(x + 1)2
D)
x(x + 1)2
Use synthetic division to divide.
227)
(x4+625) ÷ (x –5)
227)
A)
x3+5x2+25x +125 +625
x –5
B)
x3–5x2+25x –125 +1250
x –5
C)
x3+5x2+25x +125 +1250
x –5
D)
x3+5x2+25x +125
Simplify the complex fraction.
228)
1
k + 6
5
k2– 36
228)
A)
5
k – 6
B)
k + 6
5
C)
k – 6
D)
k – 6
5
Add. Simplify the result, if possible.
229)
x
x + 2 +5
x + 2
229)
A)
x + 5
x + 2
B)
5
2
C)
6x
x + 2
D)
5x
x2+ 4x +4
Find the domain of the rational function.
230)
f(x) =x – 2
6– x
230)
A)
domain of f: ( , 0) (0, )
B)
domain of f: ( , )
C)
domain of f: ( , –6) (–6, )
D)
domain of f: ( , 6) (6, )
Provide an appropriate response.
231)
Use synthetic division to decide whether –2 is a solution of 3x3+ 14x2+ 13x – 6 = 0.
231)
A)
solution
B)
not a solution
Simplify the complex fraction.
232)
49p2– 25q2
pq
7
q–5
p
232)
A)
5p + 7q
B)
5p + 7q
pq
C)
pq
7p + 5q
D)
7p + 5q
Divide.
233)
(–9x3+ 12x2– 18x + 18) ÷ (3x – 1)
233)
A)
–3x2+ 3x – 5
B)
–3x2+ 3x – 5 +16
3x – 1
C)
x2– 5 +3
3x – 1
D)
–3x2+ 3x – 5 +13
3x – 1
Perform the indicated operations. Simplify where possible.
234)
3
x –4+3– x
4– x
234)
A)
6
x –4
B)
0
C)
x –6
x –4
D)
x
x –4
Solve the problem.
235)
The function f(x) =24,000 +200x
x models the average cost per unit, f(x), for Electrostuff to
manufacture x units of Electrogadget IV. How many units must the company produce to have an
average cost per unit of $300?
235)
A)
240 units
B)
120 units
C)
200 units
D)
242 units
236)
One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 8 minutes. If
another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long
would it take the third conveyor belt alone to do the same job?
236)
A)
41
72 minute
B)
7
72 minute
C)
131
41 minutes
D)
10 2
7 minutes
Perform the indicated operations. Simplify the result, if possible.
237)
3
y2– 3y + 2
+7
y2– 1
237)
A)
10y – 11
(y – 1)(y + 1)(y – 2)
B)
10y – 11
(y – 1)(y – 2)
C)
42y – 11
(y – 1)(y + 1)(y – 2)
D)
11y – 10
(y – 1)(y + 1)(y – 2)
Write an equation to describe the variation. Use k for the constant of proportionality.
238)
p varies jointly as q and the cube of r.
238)
A)
p= kqr3
B)
p+q+r3= k
C)
pqr3= k
D)
p= k +q+r3
The graph of a rational function, f, is shown in the figure. Use the graph to answer the question.
239)
Find all vertical asymptotes of the graph.
239)
A)
y = 4, y = – 4
B)
x = – 6
C)
y = – 6
D)
x = 4, x = – 4
Provide an appropriate response.
240)
Solve: A =1
2h(B + b) for b
240)
A)
b=2A –Bh
h
B)
b=A –Bh
h
C)
b= 2A –Bh
D)
b=2A +Bh
h
Simplify the complex fraction.
241)
7
y
3
y + 9
241)
A)
y + 9
21y
B)
7(y + 9)
3y
C)
21y(y + 9)
D)
3y
7(y + 9)
242)
6x–1+(5y)–1
x–2
242)
A)
x2
6x + 5y
B)
30xy +x2
5y
C)
6xy + 5x2
y
D)
5y
30xy +x2
Solve the problem.
243)
Suppose a cost–benefit model is given by y =2925x
100 – x , where y is the cost in thousands of dollars for
removing x percent of a given pollutant. What percent of pollutant can be removed for $25,000?
243)
A)
460.8%
B)
89.5%
C)
113.3%
D)
9.0%
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6