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Math Problems
Algebra 2
Add, subtract, multiply, and divide polynomials
Factor the expression
3
p
2
−
2
p
−
5
3 p^{2}-2 p-5
3
p
2
−
2
p
−
5
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10
(
−
4
d
+
11
)
=
3
d
+
8
10(-4d+11)=3d+8
10
(
−
4
d
+
11
)
=
3
d
+
8
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P
−
P
−
1
2
=
1
−
P
−
1
3
\frac{P-P-1}{2}=\frac{1-P-1}{3}
2
P
−
P
−
1
=
3
1
−
P
−
1
Find
P
P
P
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Find
x
x
x
\newline
2
x
−
(
7
−
5
x
)
9
x
−
(
3
+
4
x
)
=
7
6
\frac{2 x-(7-5 x)}{9 x-(3+4 x)}=\frac{7}{6}
9
x
−
(
3
+
4
x
)
2
x
−
(
7
−
5
x
)
=
6
7
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Simplify
2
(
x
+
6
)
−
8
2(x+6)-8
2
(
x
+
6
)
−
8
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3
t
−
2
4
−
2
t
+
3
3
=
2
3
−
t
\frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2}{3}-t
4
3
t
−
2
−
3
2
t
+
3
=
3
2
−
t
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(
5
5
−
6
)
−
(
5
+
4
)
=
(5 \sqrt{5}-6)-(\sqrt{5}+4)=
(
5
5
−
6
)
−
(
5
+
4
)
=
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(iii)
6
(
8
)
n
+
1
+
16
(
2
)
3
n
−
2
10
(
2
)
3
n
+
1
−
7
(
8
)
n
\frac{6(8)^{n+1}+16(2)^{3 n-2}}{10(2)^{3 n+1}-7(8)^{n}}
10
(
2
)
3
n
+
1
−
7
(
8
)
n
6
(
8
)
n
+
1
+
16
(
2
)
3
n
−
2
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Ten students sit together. Reatlife-Problem
\newline
(a) In how many ways can they sit if they sit in a row?
\newline
10
!
=
3628800
10! = 3628800
10
!
=
3628800
\newline
(b) In how many ways can they sit if they sit in two rows with five seats each?
\newline
Hint
4
4
4
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3
(
4
i
−
1
)
+
2
(
i
+
3
)
=
9
+
5
(
i
−
3
)
−
9
3(4 i-1)+2(i+3)=9+5(i-3)-9
3
(
4
i
−
1
)
+
2
(
i
+
3
)
=
9
+
5
(
i
−
3
)
−
9
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2
(
3
c
−
2
)
=
c
+
2
(
2
c
+
4
)
2(3 c-2)=c+2(2 c+4)
2
(
3
c
−
2
)
=
c
+
2
(
2
c
+
4
)
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Your answer should be a polynomial.
(
x
2
−
9
)
/
(
x
−
3
)
(x^2-9)/(x-3)
(
x
2
−
9
)
/
(
x
−
3
)
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2
x
2
+
11
x
−
9
2
x
−
3
\frac{2x^{2}+11x-9}{2x-3}
2
x
−
3
2
x
2
+
11
x
−
9
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3
x
2
+
x
−
6
4
=
2
\frac{3x}{2}+\frac{x-6}{4}=2
2
3
x
+
4
x
−
6
=
2
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f
(
x
)
=
2
x
−
3
x
3
+
3
x
f(x)=\frac{2 x-3}{x^{3}+3 x}
f
(
x
)
=
x
3
+
3
x
2
x
−
3
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5
x
−
3
2
+
7
4
=
7
x
−
3
6
+
5
2
\frac{5 x-3}{2}+\frac{7}{4}=\frac{7 x-3}{6}+\frac{5}{2}
2
5
x
−
3
+
4
7
=
6
7
x
−
3
+
2
5
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2
2
2
)
(
4
x
−
5
)
(
4
x
+
5
)
−
(
4
x
−
1
)
2
=
9
−
2
x
(4 x-5)(4 x+5)-(4 x-1)^{2}=9-2 x
(
4
x
−
5
)
(
4
x
+
5
)
−
(
4
x
−
1
)
2
=
9
−
2
x
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(
5
x
−
9
)
(
10
x
+
3
)
(5x-9)(10x+3)
(
5
x
−
9
)
(
10
x
+
3
)
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Multiply.
(
7
+
4
2
)
(
2
7
−
3
2
)
(\sqrt{7}+4 \sqrt{2})(2 \sqrt{7}-3 \sqrt{2})
(
7
+
4
2
)
(
2
7
−
3
2
)
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lim
x
→
−
7
x
+
7
∣
x
+
7
∣
\lim _{x \rightarrow-7} \frac{x+7}{|x+7|}
lim
x
→
−
7
∣
x
+
7∣
x
+
7
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4
+
(
2
×
6
)
−
7
(
3
+
2
)
4+(2 \times 6)-7(3+2)
4
+
(
2
×
6
)
−
7
(
3
+
2
)
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f)
7
x
2
−
13
x
25
x
2
−
9
:
(
2
5
x
2
−
3
x
−
3
2
x
−
4
3
−
5
x
)
\frac{7 x^{2}-13 x}{25 x^{2}-9}:\left(\frac{2}{5 x^{2}-3 x}-\frac{3}{2 x}-\frac{4}{3-5 x}\right)
25
x
2
−
9
7
x
2
−
13
x
:
(
5
x
2
−
3
x
2
−
2
x
3
−
3
−
5
x
4
)
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Add:
\newline
3
(
1
2
)
+
4
(
1
4
)
+
(
3
5
)
3\left(\frac{1}{2}\right)+4\left(\frac{1}{4}\right)+\left(\frac{3}{5}\right)
3
(
2
1
)
+
4
(
4
1
)
+
(
5
3
)
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Simplify:
\newline
(
−
4
p
3
)
3
(-4p^{3})^{3}
(
−
4
p
3
)
3
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2
(
9
−
3
)
+
6
+
4
5
2(9-3)+\frac{6+4}{5}
2
(
9
−
3
)
+
5
6
+
4
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5
(
2
)
(
−
3
)
+
(
2
)
2
−
2
(
−
3
)
2
5(2)(-3)+(2)^2-2(-3)^2
5
(
2
)
(
−
3
)
+
(
2
)
2
−
2
(
−
3
)
2
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10
x
8
y
4
−
6
x
4
y
5
\frac{10 x^{8} y^{4}}{-6 x^{4} y^{5}}
−
6
x
4
y
5
10
x
8
y
4
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(
3
n
4
)
2
\left(3 n^{4}\right)^{2}
(
3
n
4
)
2
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∴
4
x
3
−
6
x
2
−
20
=
1
\therefore 4 x^{3}-6 x^{2}-20=1
∴
4
x
3
−
6
x
2
−
20
=
1
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Solve for
u
u
u
.
\newline
3
u
2
=
−
7
u
−
4
3 u^{2}=-7 u-4
3
u
2
=
−
7
u
−
4
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2
x
−
2
x
(
x
2
144
)
=
0
2 x-2 x\left(\frac{x^{2}}{144}\right)=0
2
x
−
2
x
(
144
x
2
)
=
0
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x
2
−
12
x
+
36
3
x
−
18
\frac{x^{2}-12 x+36}{3 x-18}
3
x
−
18
x
2
−
12
x
+
36
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2
2
2
)
1
0
2
−
16
÷
8
10^{2}-16 \div 8
1
0
2
−
16
÷
8
\newline
3
3
3
)
(
25
+
11
)
×
2
(25+11) \times 2
(
25
+
11
)
×
2
\newline
4
4
4
)
3
+
6
×
(
5
+
4
)
÷
3
−
7
3+6 \times(5+4) \div 3-7
3
+
6
×
(
5
+
4
)
÷
3
−
7
\newline
5
5
5
)
56
−
2
(
20
+
12
÷
4
×
3
−
2
×
2
)
+
10
56-2(20+12 \div 4 \times 3-2 \times 2)+10
56
−
2
(
20
+
12
÷
4
×
3
−
2
×
2
)
+
10
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Simplify
\newline
x
2
−
4
x
(
x
+
3
)
(
5
x
−
20
)
\frac{x^{2}-4x}{(x+3)(5x-20)}
(
x
+
3
)
(
5
x
−
20
)
x
2
−
4
x
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Simplify.
\newline
(
−
w
2
+
6
w
−
4
)
+
(
2
w
2
+
7
w
+
3
)
\left(-w^{2}+6 w-4\right)+\left(2 w^{2}+7 w+3\right)
(
−
w
2
+
6
w
−
4
)
+
(
2
w
2
+
7
w
+
3
)
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11
x
(
−
9
+
10
y
)
11x(-9+10y)
11
x
(
−
9
+
10
y
)
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4
x
2
−
x
−
3
(
−
2
)
4x^2 - x-3 (-2)
4
x
2
−
x
−
3
(
−
2
)
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3
w
4
−
300
3 w^{4}-300
3
w
4
−
300
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Which is equal to
1
7
3
\frac{1}{7^3}
7
3
1
?
\newline
Choices:
\newline
(A)
(
−
7
)
3
(-7)^3
(
−
7
)
3
\newline
(B)
−
7
3
-7^3
−
7
3
\newline
(C)
7
−
3
7^{-3}
7
−
3
\newline
(D)
−
1
7
−
3
-\frac{1}{7^{-3}}
−
7
−
3
1
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14
14
14
)
(
4
×
1
0
−
5
)
−
6
\left(4 \times 10^{-5}\right)^{-6}
(
4
×
1
0
−
5
)
−
6
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Solve for
x
x
x
.
\newline
2
x
2
+
6
=
−
7
x
2 x^{2}+6=-7 x
2
x
2
+
6
=
−
7
x
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Solve for
w
w
w
.
\newline
3
w
2
−
2
=
5
w
3 w^{2}-2=5 w
3
w
2
−
2
=
5
w
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a
(
4
a
+
3
)
a(4 a+3)
a
(
4
a
+
3
)
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2
n
−
1
)
3
=
1
+
3
n
−
6
4
\frac{2 n-1)}{3}=1+\frac{3 n-6}{4}
3
2
n
−
1
)
=
1
+
4
3
n
−
6
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4
x
2
+
12
x
3
+
2
x
4
(
−
x
+
x
\frac{4 x^{2}+12 x^{3}+2 x^{4}}{(-x+x}
(
−
x
+
x
4
x
2
+
12
x
3
+
2
x
4
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−
2
x
2
+
10
x
−
2
(
x
2
−
1
)
2
\frac{-2 x^{2}+10 x-2}{\left(x^{2}-1\right)^{2}}
(
x
2
−
1
)
2
−
2
x
2
+
10
x
−
2
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−
1
(
2
x
−
8
)
2
=
−
144
-1(2x-8)^2=-144
−
1
(
2
x
−
8
)
2
=
−
144
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z
+
1
z
−
2
=
z
+
8
z
−
4
\frac{z+1}{z-2}=\frac{z+8}{z-4}
z
−
2
z
+
1
=
z
−
4
z
+
8
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g
(
7
−
d
)
g(7-d)
g
(
7
−
d
)
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−
6.3
p
+
(
−
3.6
)
−
(
−
8.5
)
−
(
−
4.2
)
-6.3p + (-3.6) - (-8.5) - (-4.2)
−
6.3
p
+
(
−
3.6
)
−
(
−
8.5
)
−
(
−
4.2
)
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1
2
3
...
10
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