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Math Problems
Algebra 2
Composition of linear and quadratic functions: find an equation
The form of your answer should either be
p
(
x
)
p(x)
p
(
x
)
or
p
(
x
)
+
k
x
−
5
p(x)+\frac{k}{x-5}
p
(
x
)
+
x
−
5
k
where
p
(
x
)
p(x)
p
(
x
)
is a polynomial and
k
k
k
is an integer.
2
x
3
−
11
x
2
+
25
x
−
5
\frac{2x^3-11x^2+25}{x-5}
x
−
5
2
x
3
−
11
x
2
+
25
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The form of your answer should either be
p
(
x
)
p(x)
p
(
x
)
or
p
(
x
)
+
k
x
−
3
p(x)+\frac{k}{x-3}
p
(
x
)
+
x
−
3
k
where
p
(
x
)
p(x)
p
(
x
)
is a polynomial and
k
k
k
is an integer.
4
x
3
−
14
x
2
−
7
x
−
4
x
−
4
\frac{4x^3-14x^2-7x-4}{x-4}
x
−
4
4
x
3
−
14
x
2
−
7
x
−
4
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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.
x
2
+
5
x
+
5
x
+
3
\frac{x^2+5x+5}{x+3}
x
+
3
x
2
+
5
x
+
5
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Your answer should be a polynomial
(
x
2
−
16
)
/
(
x
+
4
)
(x^2-16)/(x+4)
(
x
2
−
16
)
/
(
x
+
4
)
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Your answer should be a polynomial
(
x
2
+
11
x
+
18
)
/
(
x
+
2
)
(x^2+11x+18)/(x+2)
(
x
2
+
11
x
+
18
)
/
(
x
+
2
)
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Your answer should be a polynomial
(
x
2
+
10
x
+
25
)
/
(
x
+
5
)
(x^2+10x+25)/(x+5)
(
x
2
+
10
x
+
25
)
/
(
x
+
5
)
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Your answer should be a polynomial.
(
x
2
−
7
x
+
12
)
/
(
x
−
3
)
(x^2-7x+12)/(x-3)
(
x
2
−
7
x
+
12
)
/
(
x
−
3
)
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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.
6
x
5
−
2
x
4
−
1
x
=
\frac{6x^5-2x^4-1}{x}=
x
6
x
5
−
2
x
4
−
1
=
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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.
x
5
+
6
x
+
2
x
\frac{x^5+6x+2}{x}
x
x
5
+
6
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.
2
x
3
+
7
x
=
\frac{2x^3+7}{x}=
x
2
x
3
+
7
=
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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.
6
x
2
−
4
x
−
3
x
=
\frac{6x^2-4x-3}{x}=
x
6
x
2
−
4
x
−
3
=
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∠
A
=
6
x
−
3
5
∘
∠
B
=
3
x
+
5
3
∘
\angle A=6 x-35^{\circ} \quad \angle B=3 x+53^{\circ}
∠
A
=
6
x
−
3
5
∘
∠
B
=
3
x
+
5
3
∘
\newline
Solve for
x
x
x
and then find the measure of
∠
A
\angle A
∠
A
:
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Question
\newline
Factor the expression completely.
\newline
y
3
+
x
3
y
5
y^{3}+x^{3} y^{5}
y
3
+
x
3
y
5
\newline
Answer Attempt
2
2
2
out of
2
2
2
\newline
Submit Answer
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Solve for
m
m
m
. Express your answer in simplest radical form if necessary.
\newline
m
3
=
−
27
m^{3}=-27
m
3
=
−
27
\newline
Answer:
m
=
m=
m
=
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Solve for
d
d
d
. Express your answer in simplest radical form if necessary.
\newline
17
=
d
3
17=d^{3}
17
=
d
3
\newline
Answer:
d
=
d=
d
=
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Solve for
y
y
y
. Express your answer in simplest radical form if necessary.
\newline
32
=
y
2
32=y^{2}
32
=
y
2
\newline
Answer:
y
=
y=
y
=
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Solve for
m
m
m
. Express your answer in simplest radical form if necessary.
\newline
27
=
m
3
27=m^{3}
27
=
m
3
\newline
Answer:
m
=
m=
m
=
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Solve for
m
m
m
. Express your answer in simplest radical form if necessary.
\newline
−
216
=
m
3
-216=m^{3}
−
216
=
m
3
\newline
Answer:
m
=
m=
m
=
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Solve for
x
x
x
. Express your answer in simplest radical form if necessary.
\newline
121
=
x
2
121=x^{2}
121
=
x
2
\newline
Answer:
x
=
x=
x
=
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Solve for
d
d
d
. Express your answer in simplest radical form if necessary.
\newline
77
=
d
3
77=d^{3}
77
=
d
3
\newline
Answer:
d
=
d=
d
=
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y
=
x
2
+
7
x
−
5
y=x^2+7x-5
y
=
x
2
+
7
x
−
5
make
x
x
x
the subject
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Given the function
f
(
x
)
=
−
4
+
2
x
3
f(x)=-4+2 x^{3}
f
(
x
)
=
−
4
+
2
x
3
, then what is
−
2
f
(
x
)
-2 f(x)
−
2
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
4
−
x
2
f(x)=-4-x^{2}
f
(
x
)
=
−
4
−
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
x
−
x
2
f(x)=x-x^{2}
f
(
x
)
=
x
−
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
2
+
4
x
f(x)=-x^{2}+4 x
f
(
x
)
=
−
x
2
+
4
x
, then what is
f
(
x
)
−
2
f(x)-2
f
(
x
)
−
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
3
x
2
−
x
f(x)=3 x^{2}-x
f
(
x
)
=
3
x
2
−
x
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
x
−
3
x
2
f(x)=x-3 x^{2}
f
(
x
)
=
x
−
3
x
2
, then what is
−
3
f
(
x
)
-3 f(x)
−
3
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
x
2
−
4
f(x)=5 x^{2}-4
f
(
x
)
=
5
x
2
−
4
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
x
−
4
x
2
f(x)=5 x-4 x^{2}
f
(
x
)
=
5
x
−
4
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
x
2
−
1
f(x)=5 x^{2}-1
f
(
x
)
=
5
x
2
−
1
, then what is
f
(
x
)
+
3
f(x)+3
f
(
x
)
+
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
+
5
x
2
f(x)=-1+5 x^{2}
f
(
x
)
=
−
1
+
5
x
2
, then what is
f
(
x
)
−
3
f(x)-3
f
(
x
)
−
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
6
−
x
2
f(x)=-6-x^{2}
f
(
x
)
=
−
6
−
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
2
−
6
x
2
f(x)=2-6 x^{2}
f
(
x
)
=
2
−
6
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
3
+
6
x
2
f(x)=3+6 x^{2}
f
(
x
)
=
3
+
6
x
2
, then what is
f
(
−
x
)
f(-x)
f
(
−
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
6
−
x
2
f(x)=-6-x^{2}
f
(
x
)
=
−
6
−
x
2
, then what is
f
(
x
)
−
2
f(x)-2
f
(
x
)
−
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
+
3
x
2
f(x)=-1+3 x^{2}
f
(
x
)
=
−
1
+
3
x
2
, then what is
f
(
x
)
+
3
f(x)+3
f
(
x
)
+
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
6
x
3
−
4
x
f(x)=6 x^{3}-4 x
f
(
x
)
=
6
x
3
−
4
x
, then what is
f
(
x
)
+
2
f(x)+2
f
(
x
)
+
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
x
+
x
2
f(x)=-2 x+x^{2}
f
(
x
)
=
−
2
x
+
x
2
, then what is
f
(
x
−
1
)
f(x-1)
f
(
x
−
1
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
6
x
−
x
2
f(x)=6 x-x^{2}
f
(
x
)
=
6
x
−
x
2
, then what is
f
(
x
+
2
)
f(x+2)
f
(
x
+
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
−
5
x
2
f(x)=-x-5 x^{2}
f
(
x
)
=
−
x
−
5
x
2
, then what is
f
(
−
3
x
)
f(-3 x)
f
(
−
3
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
x
−
x
2
f(x)=x-x^{2}
f
(
x
)
=
x
−
x
2
, then what is
3
f
(
x
)
3 f(x)
3
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
x
3
−
x
2
f(x)=5 x^{3}-x^{2}
f
(
x
)
=
5
x
3
−
x
2
, then what is
f
(
x
)
−
1
f(x)-1
f
(
x
)
−
1
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
2
+
5
x
f(x)=-x^{2}+5 x
f
(
x
)
=
−
x
2
+
5
x
, then what is
f
(
x
−
3
)
f(x-3)
f
(
x
−
3
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
3
x
2
−
5
f(x)=3 x^{2}-5
f
(
x
)
=
3
x
2
−
5
, then what is
f
(
x
)
+
3
f(x)+3
f
(
x
)
+
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
+
3
x
2
f(x)=-1+3 x^{2}
f
(
x
)
=
−
1
+
3
x
2
, then what is
f
(
3
x
)
f(3 x)
f
(
3
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
6
x
2
−
1
f(x)=6 x^{2}-1
f
(
x
)
=
6
x
2
−
1
, then what is
f
(
−
x
)
f(-x)
f
(
−
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
+
6
x
3
f(x)=-x+6 x^{3}
f
(
x
)
=
−
x
+
6
x
3
, then what is
f
(
x
)
−
2
f(x)-2
f
(
x
)
−
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
x
2
−
x
f(x)=-2 x^{2}-x
f
(
x
)
=
−
2
x
2
−
x
, then what is
f
(
x
)
+
2
f(x)+2
f
(
x
)
+
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
4
x
2
+
5
f(x)=-4 x^{2}+5
f
(
x
)
=
−
4
x
2
+
5
, then what is
f
(
x
−
2
)
f(x-2)
f
(
x
−
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
+
5
x
2
f(x)=-2+5 x^{2}
f
(
x
)
=
−
2
+
5
x
2
, then what is
f
(
x
)
−
1
f(x)-1
f
(
x
)
−
1
as a simplified polynomial?
\newline
Answer:
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