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Precalculus
Rational root theorem
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
−
5
-5
−
5
and a constant term of
−
2
-2
−
2
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
2
-2
−
2
\newline
(C)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(D)
1
1
1
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
−
7
-7
−
7
and a constant term of
−
3
-3
−
3
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
1
1
1
\newline
(B)
1
7
\frac{1}{7}
7
1
\newline
(C)
−
3
-3
−
3
\newline
(D)
1
2
\frac{1}{2}
2
1
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
2
2
2
and a constant term of
1
1
1
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
4
3
\frac{4}{3}
3
4
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
1
1
1
\newline
(D)
1
10
\frac{1}{10}
10
1
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
−
1
-1
−
1
and a constant term of
3
3
3
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
-1
−
1
\newline
(B)
1
1
1
\newline
(C)
−
7
-7
−
7
\newline
(D)
−
3
-3
−
3
Get tutor help
A polynomial function
h
(
x
)
h(x)
h
(
x
)
with integer coefficients has a leading coefficient of
8
8
8
and a constant term of
2
2
2
. According to the Rational Root Theorem, which of the following are possible roots of
h
(
x
)
h(x)
h
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
1
8
\frac{1}{8}
8
1
\newline
(B)
2
2
2
\newline
(C)
1
4
\frac{1}{4}
4
1
\newline
(D)
−
18
17
-\frac{18}{17}
−
17
18
Get tutor help
A polynomial function
h
(
x
)
h(x)
h
(
x
)
with integer coefficients has a leading coefficient of
2
2
2
and a constant term of
−
7
-7
−
7
. According to the Rational Root Theorem, which of the following are possible roots of
h
(
x
)
h(x)
h
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
1
2
-\frac{1}{2}
−
2
1
\newline
(C)
−
7
-7
−
7
\newline
(D)
7
3
\frac{7}{3}
3
7
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
−
2
-2
−
2
and a constant term of
8
8
8
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
12
7
-\frac{12}{7}
−
7
12
\newline
(B)
11
20
\frac{11}{20}
20
11
\newline
(C)
−
5
3
-\frac{5}{3}
−
3
5
\newline
(D)
1
1
1
Get tutor help
A polynomial function
h
(
x
)
h(x)
h
(
x
)
with integer coefficients has a leading coefficient of
7
7
7
and a constant term of
2
2
2
. According to the Rational Root Theorem, which of the following are possible roots of
h
(
x
)
h(x)
h
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
13
-\frac{1}{13}
−
13
1
\newline
(B)
18
7
\frac{18}{7}
7
18
\newline
(C)
−
2
7
-\frac{2}{7}
−
7
2
\newline
(D)
1
4
\frac{1}{4}
4
1
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
7
7
7
and a constant term of
5
5
5
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
10
17
-\frac{10}{17}
−
17
10
\newline
(B)
−
5
9
-\frac{5}{9}
−
9
5
\newline
(C)
−
8
-8
−
8
\newline
(D)
−
1
-1
−
1
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
1
1
1
and a constant term of
−
16
-16
−
16
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
14
-14
−
14
\newline
(C)
−
4
5
-\frac{4}{5}
−
5
4
\newline
(D)
−
3
-3
−
3
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
5
5
5
and a constant term of
−
2
-2
−
2
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
2
-2
−
2
\newline
(B)
2
2
2
\newline
(C)
1
5
\frac{1}{5}
5
1
\newline
(D)
5
13
\frac{5}{13}
13
5
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
−
14
-14
−
14
and a constant term of
1
1
1
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
15
2
\frac{15}{2}
2
15
\newline
(B)
15
7
\frac{15}{7}
7
15
\newline
(C)
−
1
2
-\frac{1}{2}
−
2
1
\newline
(D)
1
14
\frac{1}{14}
14
1
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
3
3
3
and a constant term of
1
1
1
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
1
1
1
\newline
(B)
−
1
3
-\frac{1}{3}
−
3
1
\newline
(C)
1
3
\frac{1}{3}
3
1
\newline
(D)
−
19
-19
−
19
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
−
5
-5
−
5
and a constant term of
2
2
2
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(B)
2
17
\frac{2}{17}
17
2
\newline
(C)
2
2
2
\newline
(D)
10
3
\frac{10}{3}
3
10
Get tutor help
A polynomial function
h
(
x
)
h(x)
h
(
x
)
with integer coefficients has a leading coefficient of
−
1
-1
−
1
and a constant term of
7
7
7
. According to the Rational Root Theorem, which of the following are possible roots of
h
(
x
)
h(x)
h
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
1
1
1
\newline
(B)
7
7
7
\newline
(C)
−
7
-7
−
7
\newline
(D)
−
1
-1
−
1
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
1
1
1
and a constant term of
14
14
14
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
8
19
\frac{8}{19}
19
8
\newline
(B)
3
2
\frac{3}{2}
2
3
\newline
(C)
−
2
-2
−
2
\newline
(D)
−
1
-1
−
1
Get tutor help
A polynomial function
h
(
x
)
h(x)
h
(
x
)
with integer coefficients has a leading coefficient of
16
16
16
and a constant term of
−
1
-1
−
1
. According to the Rational Root Theorem, which of the following are possible roots of
h
(
x
)
h(x)
h
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
18
5
\frac{18}{5}
5
18
\newline
(B)
−
18
-18
−
18
\newline
(C)
7
7
7
\newline
(D)
1
1
1
Get tutor help
A polynomial function
g
(
x
)
g(x)
g
(
x
)
with integer coefficients has a leading coefficient of
−
7
-7
−
7
and a constant term of
−
3
-3
−
3
. According to the Rational Root Theorem, which of the following are possible roots of
g
(
x
)
g(x)
g
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
1
7
-\frac{1}{7}
−
7
1
\newline
(C)
1
7
\frac{1}{7}
7
1
\newline
(D)
1
1
1
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
1
1
1
and a constant term of
−
14
-14
−
14
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
7
-7
−
7
\newline
(B)
7
2
\frac{7}{2}
2
7
\newline
(C)
14
14
14
\newline
(D)
−
14
-14
−
14
Get tutor help
A polynomial function
f
(
x
)
f(x)
f
(
x
)
with integer coefficients has a leading coefficient of
2
2
2
and a constant term of
−
7
-7
−
7
. According to the Rational Root Theorem, which of the following are possible roots of
f
(
x
)
f(x)
f
(
x
)
?
\newline
Multi-select Choices:
\newline
(A)
−
1
-1
−
1
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
−
1
2
-\frac{1}{2}
−
2
1
\newline
(D)
−
7
2
-\frac{7}{2}
−
2
7
Get tutor help
