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Math Problems
Algebra 2
Factor sums and differences of cubes
Divide the polynomials.
\newline
Your answer should be a polynomial.
\newline
x
2
+
7
x
+
10
x
+
2
=
\frac{x^{2}+7 x+10}{x+2}=
x
+
2
x
2
+
7
x
+
10
=
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Divide the polynomials.
\newline
Your answer should be a polynomial.
\newline
x
2
−
12
x
+
20
x
−
10
=
\frac{x^{2}-12 x+20}{x-10}=
x
−
10
x
2
−
12
x
+
20
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
4
x
+
7
+
8
x
−
1
=
\frac{4}{x+7}+\frac{8}{x-1}=
x
+
7
4
+
x
−
1
8
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
4
9
x
2
−
45
x
−
6
x
x
2
−
25
=
\frac{4}{9 x^{2}-45 x}-\frac{6 x}{x^{2}-25}=
9
x
2
−
45
x
4
−
x
2
−
25
6
x
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
2
x
−
3
+
5
x
+
1
=
\frac{2}{x-3}+\frac{5}{x+1}=
x
−
3
2
+
x
+
1
5
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
4
3
x
2
+
15
x
+
7
x
x
2
+
10
x
+
25
=
\frac{4}{3 x^{2}+15 x}+\frac{7 x}{x^{2}+10 x+25}=
3
x
2
+
15
x
4
+
x
2
+
10
x
+
25
7
x
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
8
x
x
2
−
49
+
5
x
2
−
4
x
−
21
=
\frac{8 x}{x^{2}-49}+\frac{5}{x^{2}-4 x-21}=
x
2
−
49
8
x
+
x
2
−
4
x
−
21
5
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
8
x
x
2
+
8
x
+
16
−
6
x
2
+
4
x
=
\frac{8 x}{x^{2}+8 x+16}-\frac{6}{x^{2}+4 x}=
x
2
+
8
x
+
16
8
x
−
x
2
+
4
x
6
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
9
x
2
−
8
x
−
9
−
2
x
2
−
81
=
\frac{9}{x^{2}-8 x-9}-\frac{2}{x^{2}-81}=
x
2
−
8
x
−
9
9
−
x
2
−
81
2
=
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Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
2
x
x
2
−
3
x
−
18
−
5
x
2
+
6
x
+
9
=
\frac{2 x}{x^{2}-3 x-18}-\frac{5}{x^{2}+6 x+9}=
x
2
−
3
x
−
18
2
x
−
x
2
+
6
x
+
9
5
=
Get tutor help
Subtract.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
3
x
2
−
49
−
9
x
2
−
14
x
+
49
=
\frac{3}{x^{2}-49}-\frac{9}{x^{2}-14 x+49}=
x
2
−
49
3
−
x
2
−
14
x
+
49
9
=
Get tutor help
Add.
\newline
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
\newline
9
x
2
−
12
x
+
36
+
x
x
2
−
36
=
\frac{9}{x^{2}-12 x+36}+\frac{x}{x^{2}-36}=
x
2
−
12
x
+
36
9
+
x
2
−
36
x
=
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x
3
+
25
x
2
+
50
x
−
1000
x^{3}+25 x^{2}+50 x-1000
x
3
+
25
x
2
+
50
x
−
1000
\newline
The polynomial has
(
x
−
5
)
(x-5)
(
x
−
5
)
and
(
x
+
10
)
(x+10)
(
x
+
10
)
as factors. What is the remaining factor?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
x
+
2
)
(x+2)
(
x
+
2
)
\newline
(B)
(
x
−
2
)
(x-2)
(
x
−
2
)
\newline
(C)
(
x
+
20
)
(x+20)
(
x
+
20
)
\newline
(D)
(
x
−
20
)
(x-20)
(
x
−
20
)
Get tutor help
Factor completely.
\newline
(
x
2
+
x
−
6
)
(
2
x
2
+
4
x
)
=
\left(x^{2}+x-6\right)\left(2 x^{2}+4 x\right)=
(
x
2
+
x
−
6
)
(
2
x
2
+
4
x
)
=
Get tutor help
Factor completely.
\newline
(
x
2
−
4
)
(
x
2
+
6
x
+
9
)
=
\left(x^{2}-4\right)\left(x^{2}+6 x+9\right)=
(
x
2
−
4
)
(
x
2
+
6
x
+
9
)
=
Get tutor help
Factor completely.
\newline
(
x
2
−
5
x
+
4
)
(
x
2
−
9
)
=
\left(x^{2}-5 x+4\right)\left(x^{2}-9\right)=
(
x
2
−
5
x
+
4
)
(
x
2
−
9
)
=
Get tutor help
Factor the polynomial by its greatest common monomial factor.
\newline
6
x
3
+
8
x
2
−
4
x
=
6 x^{3}+8 x^{2}-4 x=
6
x
3
+
8
x
2
−
4
x
=
Get tutor help
Factor the polynomial by its greatest common monomial factor.
\newline
9
b
8
+
24
b
3
=
9 b^{8}+24 b^{3}=
9
b
8
+
24
b
3
=
Get tutor help
Factor the polynomial by its greatest common monomial factor.
\newline
3
b
5
+
15
b
4
−
18
b
7
=
3 b^{5}+15 b^{4}-18 b^{7}=
3
b
5
+
15
b
4
−
18
b
7
=
Get tutor help
Factor the polynomial by its greatest common monomial factor.
\newline
44
k
5
−
66
k
4
+
77
k
3
=
44 k^{5}-66 k^{4}+77 k^{3}=
44
k
5
−
66
k
4
+
77
k
3
=
Get tutor help
Factor the polynomial by its greatest common monomial factor.
\newline
14
x
2
+
28
x
5
=
14 x^{2}+28 x^{5}=
14
x
2
+
28
x
5
=
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If
64
x
2
+
p
x
+
81
=
(
8
x
+
q
)
2
64 x^{2}+p x+81=(8 x+q)^{2}
64
x
2
+
p
x
+
81
=
(
8
x
+
q
)
2
, where
p
p
p
and
q
q
q
are positive constants, what is the value of
p
q
\frac{p}{q}
q
p
?
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If
7
a
=
7
8
7^{a}=\sqrt[8]{7}
7
a
=
8
7
, what is the value of
a
a
a
?
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If
3
a
=
3
5
3^{a}=\sqrt[5]{3}
3
a
=
5
3
, what is the value of
a
a
a
?
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If
1
1
a
=
11
7
11^{a}=\sqrt[7]{11}
1
1
a
=
7
11
, what is the value of
a
a
a
?
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If
2
a
=
2
4
9
2^{a}=\sqrt[9]{2^{4}}
2
a
=
9
2
4
, what is the value of
a
a
a
?
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If
7
a
=
7
3
7^{a}=\sqrt[3]{7}
7
a
=
3
7
, what is the value of
a
a
a
?
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If
5
a
=
5
2
3
5^{a}=\sqrt[3]{5^{2}}
5
a
=
3
5
2
, what is the value of
a
a
a
?
Get tutor help
Divide the polynomials.
\newline
Your answer should be a polynomial.
\newline
x
4
+
5
x
3
+
3
x
2
x
=
\frac{x^{4}+5 x^{3}+3 x^{2}}{x}=
x
x
4
+
5
x
3
+
3
x
2
=
Get tutor help
Divide the polynomials. Your answer should be a polynomial.
\newline
x
2
+
2
x
x
=
□
\frac{x^{2}+2 x}{x}=\square
x
x
2
+
2
x
=
□
Get tutor help
Divide the polynomials. Your answer should be a polynomial.
\newline
x
5
−
3
x
2
+
2
x
x
=
\frac{x^{5}-3 x^{2}+2 x}{x}=
x
x
5
−
3
x
2
+
2
x
=
Get tutor help
Divide the polynomials. Your answer should be a polynomial.
\newline
2
x
5
+
5
x
3
x
=
\frac{2 x^{5}+5 x^{3}}{x}=
x
2
x
5
+
5
x
3
=
Get tutor help
Divide the polynomials.
\newline
Your answer should be a polynomial.
\newline
2
x
4
+
4
x
3
−
x
2
x
=
\frac{2 x^{4}+4 x^{3}-x^{2}}{x}=
x
2
x
4
+
4
x
3
−
x
2
=
Get tutor help
Divide the polynomials.
\newline
Your answer should be a polynomial.
\newline
3
x
5
+
x
4
−
4
x
2
x
=
\frac{3 x^{5}+x^{4}-4 x^{2}}{x}=
x
3
x
5
+
x
4
−
4
x
2
=
Get tutor help
Divide the polynomials. Your answer should be a polynomial.
\newline
4
x
3
+
x
2
x
=
□
\frac{4 x^{3}+x^{2}}{x}=\square
x
4
x
3
+
x
2
=
□
Get tutor help
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
6
x
5
−
2
x
4
−
1
x
=
\frac{6 x^{5}-2 x^{4}-1}{x}=
x
6
x
5
−
2
x
4
−
1
=
Get tutor help
Divide the polynomials. Your answer should be a polynomial.
\newline
x
3
−
5
x
2
x
=
□
\frac{x^{3}-5 x^{2}}{x}=\square
x
x
3
−
5
x
2
=
□
Get tutor help
Find the binomial that completes the factorization.
\newline
t
3
+
u
3
=
(
‾
)
(
t
2
−
t
u
+
u
2
)
t^3 + u^3 = (\underline{\hspace{1cm}}) (t^2 - tu + u^2)
t
3
+
u
3
=
(
)
(
t
2
−
t
u
+
u
2
)
Get tutor help
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