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Math Problems
Precalculus
Operations with rational exponents
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
3
x
)
2
−
22
(
x
2
−
3
x
)
+
72
\left(x^{2}-3 x\right)^{2}-22\left(x^{2}-3 x\right)+72
(
x
2
−
3
x
)
2
−
22
(
x
2
−
3
x
)
+
72
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
7
x
)
2
+
4
(
x
2
−
7
x
)
−
96
\left(x^{2}-7 x\right)^{2}+4\left(x^{2}-7 x\right)-96
(
x
2
−
7
x
)
2
+
4
(
x
2
−
7
x
)
−
96
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
3
x
)
2
−
16
(
x
2
−
3
x
)
−
36
\left(x^{2}-3 x\right)^{2}-16\left(x^{2}-3 x\right)-36
(
x
2
−
3
x
)
2
−
16
(
x
2
−
3
x
)
−
36
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
+
3
x
)
2
−
22
(
x
2
+
3
x
)
+
72
\left(x^{2}+3 x\right)^{2}-22\left(x^{2}+3 x\right)+72
(
x
2
+
3
x
)
2
−
22
(
x
2
+
3
x
)
+
72
\newline
Answer:
Get tutor help
Factor completely.
\newline
−
7
x
4
y
3
z
4
+
41
x
6
y
5
z
7
-7 x^{4} y^{3} z^{4}+41 x^{6} y^{5} z^{7}
−
7
x
4
y
3
z
4
+
41
x
6
y
5
z
7
\newline
Answer:
Get tutor help
Factor completely.
\newline
−
21
y
2
z
2
+
35
x
3
z
4
-21 y^{2} z^{2}+35 x^{3} z^{4}
−
21
y
2
z
2
+
35
x
3
z
4
\newline
Answer:
Get tutor help
Factor completely.
\newline
21
x
3
y
3
z
2
−
14
y
4
z
4
21 x^{3} y^{3} z^{2}-14 y^{4} z^{4}
21
x
3
y
3
z
2
−
14
y
4
z
4
\newline
Answer:
Get tutor help
Factor completely.
\newline
48
x
3
z
4
−
44
x
6
y
z
3
48 x^{3} z^{4}-44 x^{6} y z^{3}
48
x
3
z
4
−
44
x
6
y
z
3
\newline
Answer:
Get tutor help
Factor completely.
\newline
11
x
3
y
2
z
2
−
22
x
2
z
5
11 x^{3} y^{2} z^{2}-22 x^{2} z^{5}
11
x
3
y
2
z
2
−
22
x
2
z
5
\newline
Answer:
Get tutor help
Factor completely.
\newline
27
x
3
y
2
z
5
+
17
y
6
z
27 x^{3} y^{2} z^{5}+17 y^{6} z
27
x
3
y
2
z
5
+
17
y
6
z
\newline
Answer:
Get tutor help
Factor completely.
\newline
35
x
7
y
4
z
7
+
43
x
4
y
5
z
3
35 x^{7} y^{4} z^{7}+43 x^{4} y^{5} z^{3}
35
x
7
y
4
z
7
+
43
x
4
y
5
z
3
\newline
Answer:
Get tutor help
Factor completely.
\newline
−
28
x
4
y
3
z
3
−
21
x
6
y
6
z
4
-28 x^{4} y^{3} z^{3}-21 x^{6} y^{6} z^{4}
−
28
x
4
y
3
z
3
−
21
x
6
y
6
z
4
\newline
Answer:
Get tutor help
Factor completely.
\newline
45
x
5
y
6
+
27
x
4
y
4
z
3
45 x^{5} y^{6}+27 x^{4} y^{4} z^{3}
45
x
5
y
6
+
27
x
4
y
4
z
3
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
7
x
2
−
10
x
)
2
−
14
(
7
x
2
−
10
x
)
−
51
\left(7 x^{2}-10 x\right)^{2}-14\left(7 x^{2}-10 x\right)-51
(
7
x
2
−
10
x
)
2
−
14
(
7
x
2
−
10
x
)
−
51
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
10
x
2
+
3
x
)
2
−
19
(
10
x
2
+
3
x
)
+
18
\left(10 x^{2}+3 x\right)^{2}-19\left(10 x^{2}+3 x\right)+18
(
10
x
2
+
3
x
)
2
−
19
(
10
x
2
+
3
x
)
+
18
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
3
x
2
−
10
x
)
2
−
10
(
3
x
2
−
10
x
)
−
39
\left(3 x^{2}-10 x\right)^{2}-10\left(3 x^{2}-10 x\right)-39
(
3
x
2
−
10
x
)
2
−
10
(
3
x
2
−
10
x
)
−
39
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
3
x
2
−
14
x
)
2
−
22
(
3
x
2
−
14
x
)
+
85
\left(3 x^{2}-14 x\right)^{2}-22\left(3 x^{2}-14 x\right)+85
(
3
x
2
−
14
x
)
2
−
22
(
3
x
2
−
14
x
)
+
85
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
5
x
2
−
14
x
)
2
−
22
(
5
x
2
−
14
x
)
+
57
\left(5 x^{2}-14 x\right)^{2}-22\left(5 x^{2}-14 x\right)+57
(
5
x
2
−
14
x
)
2
−
22
(
5
x
2
−
14
x
)
+
57
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
6
x
2
+
19
x
)
2
−
8
(
6
x
2
+
19
x
)
−
33
\left(6 x^{2}+19 x\right)^{2}-8\left(6 x^{2}+19 x\right)-33
(
6
x
2
+
19
x
)
2
−
8
(
6
x
2
+
19
x
)
−
33
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
7
x
2
+
15
x
)
2
−
16
(
7
x
2
+
15
x
)
−
36
\left(7 x^{2}+15 x\right)^{2}-16\left(7 x^{2}+15 x\right)-36
(
7
x
2
+
15
x
)
2
−
16
(
7
x
2
+
15
x
)
−
36
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
3
x
2
−
5
x
)
2
−
20
(
3
x
2
−
5
x
)
+
96
\left(3 x^{2}-5 x\right)^{2}-20\left(3 x^{2}-5 x\right)+96
(
3
x
2
−
5
x
)
2
−
20
(
3
x
2
−
5
x
)
+
96
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
8
x
2
+
11
x
)
2
−
16
(
8
x
2
+
11
x
)
−
57
\left(8 x^{2}+11 x\right)^{2}-16\left(8 x^{2}+11 x\right)-57
(
8
x
2
+
11
x
)
2
−
16
(
8
x
2
+
11
x
)
−
57
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
3
x
2
−
7
x
)
2
−
16
(
3
x
2
−
7
x
)
+
60
\left(3 x^{2}-7 x\right)^{2}-16\left(3 x^{2}-7 x\right)+60
(
3
x
2
−
7
x
)
2
−
16
(
3
x
2
−
7
x
)
+
60
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
5
x
2
−
9
x
)
2
−
16
(
5
x
2
−
9
x
)
+
28
\left(5 x^{2}-9 x\right)^{2}-16\left(5 x^{2}-9 x\right)+28
(
5
x
2
−
9
x
)
2
−
16
(
5
x
2
−
9
x
)
+
28
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
3
x
2
+
13
x
)
2
+
18
(
3
x
2
+
13
x
)
+
56
\left(3 x^{2}+13 x\right)^{2}+18\left(3 x^{2}+13 x\right)+56
(
3
x
2
+
13
x
)
2
+
18
(
3
x
2
+
13
x
)
+
56
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
6
x
2
−
11
x
)
2
−
12
(
6
x
2
−
11
x
)
−
85
\left(6 x^{2}-11 x\right)^{2}-12\left(6 x^{2}-11 x\right)-85
(
6
x
2
−
11
x
)
2
−
12
(
6
x
2
−
11
x
)
−
85
\newline
Answer:
Get tutor help
Factor completely.
\newline
13
y
3
z
2
−
14
x
3
y
7
z
3
13 y^{3} z^{2}-14 x^{3} y^{7} z^{3}
13
y
3
z
2
−
14
x
3
y
7
z
3
\newline
Answer:
Get tutor help
Factor completely.
\newline
27
x
4
y
2
+
37
x
z
3
27 x^{4} y^{2}+37 x z^{3}
27
x
4
y
2
+
37
x
z
3
\newline
Answer:
Get tutor help
Factor completely.
\newline
14
x
2
y
5
z
3
+
3
y
4
14 x^{2} y^{5} z^{3}+3 y^{4}
14
x
2
y
5
z
3
+
3
y
4
\newline
Answer:
Get tutor help
Write in exponential notation:
\newline
8
3
8
5
\frac{8^{3}}{8^{5}}
8
5
8
3
Get tutor help
Write in exponential notation:
\newline
m
7
m
8
\frac{m^{7}}{m^{8}}
m
8
m
7
Get tutor help
32
x
4
−
50
4
x
3
−
12
x
2
−
5
x
+
15
\frac{32 x^{4}-50}{4 x^{3}-12 x^{2}-5 x+15}
4
x
3
−
12
x
2
−
5
x
+
15
32
x
4
−
50
Get tutor help
17
17
17
. Tim, Tom and Jim are triplets. Their brother Carl is exactly
3
3
3
years younger. All four are having their birthdays today.
\newline
How old can the four brothers be altogether?
\newline
(A)
53
53
53
\newline
(B)
54
54
54
\newline
(C)
56
56
56
\newline
(D)
59
59
59
\newline
(E)
60
60
60
Get tutor help
Can you solve this?
\newline
10
x
8
5
x
4
=
?
\frac{10 x^{8}}{5 x^{4}}=?
5
x
4
10
x
8
=
?
\newline
(A)
2
x
2
2 x^{2}
2
x
2
\newline
(B)
2
x
12
2 x^{12}
2
x
12
\newline
(C)
2
x
4
2 x^{4}
2
x
4
\newline
(D)
2
x
32
2 x^{32}
2
x
32
Get tutor help
x
1
+
(
x
1
⋅
y
)
=
12
x
1
+
(
x
1
⋅
y
2
)
=
30
\begin{array}{l}x_{1}+\left(x_{1} \cdot y\right)=12 \\ x_{1}+\left(x_{1} \cdot y^{2}\right)=30\end{array}
x
1
+
(
x
1
⋅
y
)
=
12
x
1
+
(
x
1
⋅
y
2
)
=
30
Get tutor help
Three points on the graph of the function
f
(
x
)
f(x)
f
(
x
)
are
{
(
0
,
6
)
,
(
1
,
7
)
,
(
2
,
10
)
}
\{(0,6),(1,7),(2,10)\}
{(
0
,
6
)
,
(
1
,
7
)
,
(
2
,
10
)}
. Which equation represents
f
(
x
)
f(x)
f
(
x
)
?
\newline
f
(
x
)
=
6
⋅
(
7
6
)
x
f(x)=6 \cdot\left(\frac{7}{6}\right)^{x}
f
(
x
)
=
6
⋅
(
6
7
)
x
\newline
f
(
x
)
=
3
x
+
4
f(x)=3 x+4
f
(
x
)
=
3
x
+
4
\newline
f
(
x
)
=
x
+
6
f(x)=x+6
f
(
x
)
=
x
+
6
\newline
f
(
x
)
=
x
2
+
6
f(x)=x^{2}+6
f
(
x
)
=
x
2
+
6
Get tutor help
Fully simplify using only positive exponents.
\newline
30
x
2
y
8
50
x
6
y
7
\frac{30 x^{2} y^{8}}{50 x^{6} y^{7}}
50
x
6
y
7
30
x
2
y
8
\newline
Answer:
Get tutor help
Fully simplify using only positive exponents.
\newline
30
x
2
y
6
x
6
y
6
\frac{30 x^{2} y}{6 x^{6} y^{6}}
6
x
6
y
6
30
x
2
y
\newline
Answer:
Get tutor help
Fully simplify using only positive exponents.
\newline
45
x
2
y
5
27
x
6
y
3
\frac{45 x^{2} y^{5}}{27 x^{6} y^{3}}
27
x
6
y
3
45
x
2
y
5
\newline
Answer:
Get tutor help
Fully simplify using only positive exponents.
\newline
18
x
8
y
30
x
4
y
7
\frac{18 x^{8} y}{30 x^{4} y^{7}}
30
x
4
y
7
18
x
8
y
\newline
Answer:
Get tutor help
Multiply.
\newline
7
x
2
(
8
x
2
+
5
)
7 x^{2}\left(8 x^{2}+5\right)
7
x
2
(
8
x
2
+
5
)
\newline
Answer:
Get tutor help
Multiply.
\newline
x
2
(
6
x
2
−
3
x
)
x^{2}\left(6 x^{2}-3 x\right)
x
2
(
6
x
2
−
3
x
)
\newline
Answer:
Get tutor help
Multiply.
\newline
10
x
2
(
−
9
x
2
+
10
x
)
10 x^{2}\left(-9 x^{2}+10 x\right)
10
x
2
(
−
9
x
2
+
10
x
)
\newline
Answer:
Get tutor help
Solve for
x
x
x
and write your answer in simplest form.
\newline
−
1
2
+
2
(
10
x
+
3
2
)
−
9
x
=
3
4
(
8
x
−
5
)
-\frac{1}{2}+2\left(10 x+\frac{3}{2}\right)-9 x=\frac{3}{4}(8 x-5)
−
2
1
+
2
(
10
x
+
2
3
)
−
9
x
=
4
3
(
8
x
−
5
)
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
and write your answer in simplest form.
\newline
−
9
x
=
−
4
x
+
5
(
−
3
5
x
+
4
5
)
−
8
-9 x=-4 x+5\left(-\frac{3}{5} x+\frac{4}{5}\right)-8
−
9
x
=
−
4
x
+
5
(
−
5
3
x
+
5
4
)
−
8
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
x
\mathrm{x}
x
.
\newline
4
5
+
x
−
6
7
=
x
−
6
35
\frac{4}{5}+\frac{x-6}{7}=\frac{x-6}{35}
5
4
+
7
x
−
6
=
35
x
−
6
\newline
Answer:
Get tutor help
Factor the expression completely.
\newline
x
5
y
4
+
x
3
y
3
x^{5} y^{4}+x^{3} y^{3}
x
5
y
4
+
x
3
y
3
\newline
Answer:
Get tutor help
Factor the expression completely.
\newline
x
4
y
3
+
x
2
y
3
x^{4} y^{3}+x^{2} y^{3}
x
4
y
3
+
x
2
y
3
\newline
Answer:
Get tutor help
Factor completely:
\newline
3
x
3
−
45
x
2
+
150
x
3 x^{3}-45 x^{2}+150 x
3
x
3
−
45
x
2
+
150
x
\newline
Answer:
Get tutor help
Factor completely.
\newline
180
x
10
−
125
x
2
180 x^{10}-125 x^{2}
180
x
10
−
125
x
2
\newline
Answer:
Get tutor help
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