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Math Problems
Algebra 1
Powers with decimal and fractional bases
Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
+
1
p(x)+\frac{k}{x+1}
p
(
x
)
+
x
+
1
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
−
2
x
−
8
x
+
1
=
\frac{x^{2}-2 x-8}{x+1}=
x
+
1
x
2
−
2
x
−
8
=
Get tutor help
Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
+
2
p(x)+\frac{k}{x+2}
p
(
x
)
+
x
+
2
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
+
7
x
+
12
x
+
2
=
\frac{x^{2}+7 x+12}{x+2}=
x
+
2
x
2
+
7
x
+
12
=
Get tutor help
Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
−
1
p(x)+\frac{k}{x-1}
p
(
x
)
+
x
−
1
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
+
6
x
−
4
x
−
1
=
\frac{x^{2}+6 x-4}{x-1}=
x
−
1
x
2
+
6
x
−
4
=
Get tutor help
Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
−
2
p(x)+\frac{k}{x-2}
p
(
x
)
+
x
−
2
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
−
3
x
+
9
x
−
2
=
\frac{x^{2}-3 x+9}{x-2}=
x
−
2
x
2
−
3
x
+
9
=
Get tutor help
Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
+
5
p(x)+\frac{k}{x+5}
p
(
x
)
+
x
+
5
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
−
28
x
+
5
=
□
\frac{x^{2}-28}{x+5}=\square
x
+
5
x
2
−
28
=
□
Get tutor help
Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
+
3
p(x)+\frac{k}{x+3}
p
(
x
)
+
x
+
3
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
+
5
x
+
5
x
+
3
=
\frac{x^{2}+5 x+5}{x+3}=
x
+
3
x
2
+
5
x
+
5
=
Get tutor help
Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
−
5
p(x)+\frac{k}{x-5}
p
(
x
)
+
x
−
5
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
2
−
9
x
+
14
x
−
5
=
\frac{x^{2}-9 x+14}{x-5}=
x
−
5
x
2
−
9
x
+
14
=
Get tutor help
Rewrite the expression in the form
k
⋅
y
n
k \cdot y^{n}
k
⋅
y
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
(
4
y
5
4
)
1
2
=
□
\left(4 \sqrt[4]{y^{5}}\right)^{\frac{1}{2}}=\square
(
4
4
y
5
)
2
1
=
□
Get tutor help
Rewrite the expression in the form
k
⋅
z
n
k \cdot z^{n}
k
⋅
z
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
(
27
z
2
3
)
1
3
=
□
\left(27 \sqrt[3]{z^{2}}\right)^{\frac{1}{3}}=\square
(
27
3
z
2
)
3
1
=
□
Get tutor help
Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
y
2
y
4
5
3
=
□
\sqrt[3]{\frac{y^{2}}{y^{\frac{4}{5}}}}=\square
3
y
5
4
y
2
=
□
Get tutor help
Rewrite the expression in the form
z
n
z^{n}
z
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
z
4
z
−
3
2
5
=
□
\sqrt[5]{z^{4} z^{-\frac{3}{2}}}=\square
5
z
4
z
−
2
3
=
□
Get tutor help
Rewrite the expression in the form
k
⋅
x
n
k \cdot x^{n}
k
⋅
x
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
(
16
x
3
)
1
4
=
□
\left(16 \sqrt{x^{3}}\right)^{\frac{1}{4}}=\square
(
16
x
3
)
4
1
=
□
Get tutor help
Rewrite the expression in the form
k
⋅
x
n
k \cdot x^{n}
k
⋅
x
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
12
x
4
x
3
=
□
\frac{12 \sqrt{x}}{4 x^{3}}=\square
4
x
3
12
x
=
□
Get tutor help
Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
x
2
x
2
3
4
=
□
\sqrt[4]{\frac{x^{2}}{x^{\frac{2}{3}}}}=\square
4
x
3
2
x
2
=
□
Get tutor help
Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
y
7
3
y
1
3
4
=
□
\sqrt[4]{y^{\frac{7}{3}} y^{\frac{1}{3}}}=\square
4
y
3
7
y
3
1
=
□
Get tutor help
Express
z
1
=
3
[
cos
(
6
0
∘
)
+
i
sin
(
6
0
∘
)
]
in
z_{1}=3\left[\cos \left(60^{\circ}\right)+i \sin \left(60^{\circ}\right)\right] \text { in }
z
1
=
3
[
cos
(
6
0
∘
)
+
i
sin
(
6
0
∘
)
]
in
rectangular form.
\newline
Express your answer in exact terms.
\newline
z
1
=
□
z_{1}=\square
z
1
=
□
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
9
x
2
+
2
2
x
−
9
=
\lim _{x \rightarrow-\infty} \frac{\sqrt{9 x^{2}+2}}{2 x-9}=
x
→
−
∞
lim
2
x
−
9
9
x
2
+
2
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
3
x
16
x
2
−
9
x
=
\lim _{x \rightarrow-\infty} \frac{3 x}{\sqrt{16 x^{2}-9 x}}=
x
→
−
∞
lim
16
x
2
−
9
x
3
x
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
5
x
2
+
6
x
16
x
4
−
5
x
2
=
\lim _{x \rightarrow-\infty} \frac{5 x^{2}+6 x}{\sqrt{16 x^{4}-5 x^{2}}}=
x
→
−
∞
lim
16
x
4
−
5
x
2
5
x
2
+
6
x
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
x
8
−
5
x
3
3
x
4
+
4
=
\lim _{x \rightarrow-\infty} \frac{\sqrt{x^{8}-5 x^{3}}}{3 x^{4}+4}=
x
→
−
∞
lim
3
x
4
+
4
x
8
−
5
x
3
=
Get tutor help
Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
9
x
6
+
4
x
2
x
3
−
1
=
\lim _{x \rightarrow \infty} \frac{\sqrt{9 x^{6}+4 x^{2}}}{x^{3}-1}=
x
→
∞
lim
x
3
−
1
9
x
6
+
4
x
2
=
Get tutor help
Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
2
x
4
−
7
4
x
8
+
7
x
5
=
\lim _{x \rightarrow \infty} \frac{2 x^{4}-7}{\sqrt{4 x^{8}+7 x^{5}}}=
x
→
∞
lim
4
x
8
+
7
x
5
2
x
4
−
7
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
9
x
6
9
x
12
+
4
x
6
=
\lim _{x \rightarrow-\infty} \frac{9 x^{6}}{\sqrt{9 x^{12}+4 x^{6}}}=
x
→
−
∞
lim
9
x
12
+
4
x
6
9
x
6
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
4
x
4
−
x
2
x
2
+
3
=
\lim _{x \rightarrow-\infty} \frac{\sqrt{4 x^{4}-x}}{2 x^{2}+3}=
x
→
−
∞
lim
2
x
2
+
3
4
x
4
−
x
=
Get tutor help
Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
16
x
4
−
3
2
x
2
+
3
=
\lim _{x \rightarrow \infty} \frac{\sqrt{16 x^{4}-3}}{2 x^{2}+3}=
x
→
∞
lim
2
x
2
+
3
16
x
4
−
3
=
Get tutor help
Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
5
x
2
+
4
4
x
4
+
5
x
=
\lim _{x \rightarrow \infty} \frac{5 x^{2}+4}{\sqrt{4 x^{4}+5 x}}=
x
→
∞
lim
4
x
4
+
5
x
5
x
2
+
4
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
x
5
+
4
x
2
x
10
+
8
x
7
=
\lim _{x \rightarrow-\infty} \frac{x^{5}+4 x^{2}}{\sqrt{x^{10}+8 x^{7}}}=
x
→
−
∞
lim
x
10
+
8
x
7
x
5
+
4
x
2
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
4
x
2
−
3
x
4
x
+
5
=
\lim _{x \rightarrow-\infty} \frac{\sqrt{4 x^{2}-3 x}}{4 x+5}=
x
→
−
∞
lim
4
x
+
5
4
x
2
−
3
x
=
Get tutor help
Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
4
x
2
+
4
x
4
x
+
1
=
\lim _{x \rightarrow \infty} \frac{\sqrt{4 x^{2}+4 x}}{4 x+1}=
x
→
∞
lim
4
x
+
1
4
x
2
+
4
x
=
Get tutor help
Find the limit as
x
x
x
approaches positive infinity.
\newline
lim
x
→
∞
3
x
−
1
x
2
−
6
=
\lim _{x \rightarrow \infty} \frac{3 x-1}{\sqrt{x^{2}-6}}=
x
→
∞
lim
x
2
−
6
3
x
−
1
=
Get tutor help
Find the limit as
x
x
x
approaches negative infinity.
\newline
lim
x
→
−
∞
5
x
3
−
3
x
4
x
6
−
7
=
\lim _{x \rightarrow-\infty} \frac{5 x^{3}-3 x}{\sqrt{4 x^{6}-7}}=
x
→
−
∞
lim
4
x
6
−
7
5
x
3
−
3
x
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
3
x
2
+
8
x
+
16
+
8
x
2
+
x
−
12
=
\frac{3}{x^{2}+8 x+16}+\frac{8}{x^{2}+x-12}=
x
2
+
8
x
+
16
3
+
x
2
+
x
−
12
8
=
Get tutor help
Rewrite the function by completing the square.
\newline
f
(
x
)
=
4
x
2
+
12
x
+
9
f
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} f(x)=4 x^{2}+12 x+9 \\ f(x)=\square(x+\square)^{2}+\square \end{array}
f
(
x
)
=
4
x
2
+
12
x
+
9
f
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
f
(
x
)
=
2
x
2
+
13
x
+
20
f
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} f(x)=2 x^{2}+13 x+20 \\ f(x)=\square(x+\square)^{2}+\square \end{array}
f
(
x
)
=
2
x
2
+
13
x
+
20
f
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
f
(
x
)
=
x
2
+
x
−
30
f
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} f(x)=x^{2}+x-30 \\ f(x)=\square(x+\square)^{2}+\square \end{array}
f
(
x
)
=
x
2
+
x
−
30
f
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
f
(
x
)
=
x
2
−
9
x
+
14
f
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} f(x)=x^{2}-9 x+14 \\ f(x)=\square(x+\square)^{2}+\square \end{array}
f
(
x
)
=
x
2
−
9
x
+
14
f
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
g
(
x
)
=
4
x
2
−
16
x
+
7
g
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} g(x)=4 x^{2}-16 x+7 \\ g(x)=\square(x+\square)^{2}+\square \end{array}
g
(
x
)
=
4
x
2
−
16
x
+
7
g
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
g
(
x
)
=
4
x
2
−
28
x
+
49
g
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} g(x)=4 x^{2}-28 x+49 \\ g(x)=\square(x+\square)^{2}+\square \end{array}
g
(
x
)
=
4
x
2
−
28
x
+
49
g
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
h
(
x
)
=
x
2
+
3
x
−
18
h
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} h(x)=x^{2}+3 x-18 \\ h(x)=\square(x+\square)^{2}+\square \end{array}
h
(
x
)
=
x
2
+
3
x
−
18
h
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
g
(
x
)
=
x
2
−
x
−
6
g
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} g(x)=x^{2}-x-6 \\ g(x)=\square(x+\square)^{2}+\square \end{array}
g
(
x
)
=
x
2
−
x
−
6
g
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
g
(
x
)
=
x
2
+
15
x
+
54
g
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} g(x)=x^{2}+15 x+54 \\ g(x)=\square(x+\square)^{2}+\square \end{array}
g
(
x
)
=
x
2
+
15
x
+
54
g
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
h
(
x
)
=
2
x
2
+
11
x
+
15
h
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} h(x)=2 x^{2}+11 x+15 \\ h(x)=\square(x+\square)^{2}+\square \end{array}
h
(
x
)
=
2
x
2
+
11
x
+
15
h
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
h
(
x
)
=
4
x
2
+
4
x
+
1
h
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} h(x)=4 x^{2}+4 x+1 \\ h(x)=\square(x+\square)^{2}+\square \end{array}
h
(
x
)
=
4
x
2
+
4
x
+
1
h
(
x
)
=
□
(
x
+
□
)
2
+
□
Get tutor help
Rewrite the function by completing the square.
\newline
f
(
x
)
=
2
x
2
+
3
x
−
2
f
(
x
)
=
□
(
x
+
□
)
2
+
□
\begin{array}{l} f(x)=2 x^{2}+3 x-2 \\ f(x)=\square(x+\square)^{2}+\square \end{array}
f
(
x
)
=
2
x
2
+
3
x
−
2
f
(
x
)
=
□
(
x
+
□
)
2
+
□
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y
=
6
x
−
30
y=6 x-30
y
=
6
x
−
30
\newline
y
=
x
2
−
18
x
+
114
y=x^{2}-18 x+114
y
=
x
2
−
18
x
+
114
\newline
If
(
a
,
b
)
(a, b)
(
a
,
b
)
is the solution to the system of equations shown, what is the value of
b
b
b
?
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−
(
5
c
)
0
+
7
1
−
2
2
-(5 c)^{0}+7^{1}-2^{2}
−
(
5
c
)
0
+
7
1
−
2
2
\newline
If
c
≠
0
c \neq 0
c
=
0
, what is the value of the given expression?
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Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
p(x)+\frac{k}{x}
p
(
x
)
+
x
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
2
x
3
+
7
x
=
□
\frac{2 x^{3}+7}{x}=\square
x
2
x
3
+
7
=
□
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Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
p(x)+\frac{k}{x}
p
(
x
)
+
x
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
3
x
3
−
x
−
2
x
=
\frac{3 x^{3}-x-2}{x}=
x
3
x
3
−
x
−
2
=
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Divide the polynomials. Your answer should be in the form
p
(
x
)
+
k
x
p(x)+\frac{k}{x}
p
(
x
)
+
x
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
3
x
2
−
10
x
=
□
\frac{3 x^{2}-10}{x}=\square
x
3
x
2
−
10
=
□
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Divide the polynomials.
\newline
Your answer should be in the form
p
(
x
)
+
k
x
p(x)+\frac{k}{x}
p
(
x
)
+
x
k
where
p
p
p
is a polynomial and
k
k
k
is an integer.
\newline
x
5
+
6
x
+
2
x
=
□
\frac{x^{5}+6 x+2}{x}=\square
x
x
5
+
6
x
+
2
=
□
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