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Math Problems
Precalculus
Factor sums and differences of cubes
(
8
8
8
pts) Factor out the greatest common factor for each problem (GC) a.
4
a
2
+
4
a
b
4a^{2}+4ab
4
a
2
+
4
ab
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Write the following number in scientific notation.
\newline
1
,
598
,
000
,
000
1,598,000,000
1
,
598
,
000
,
000
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SOLVING QUADRATIE
\newline
C. Determine the solutions of each quadratic equation using the factoring method.
\newline
x
2
+
5
x
+
6
=
0
x^{2}+5x+6=0
x
2
+
5
x
+
6
=
0
\newline
x
2
−
3
x
−
4
=
0
x^{2}-3x-4=0
x
2
−
3
x
−
4
=
0
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y
=
(
x
+
5
)
2
y=(x+5)^{2}
y
=
(
x
+
5
)
2
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1
1
1
.
8
2
x
−
9
=
8
x
8^{2 x-9}=8^{x}
8
2
x
−
9
=
8
x
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p
=
1
2
k
x
2
p=\frac{1}{2} k x^{2}
p
=
2
1
k
x
2
\newline
As springs compress or stretch, potential energy in joules,
p
p
p
, is stored in them according to the given equation, where
k
k
k
is the spring constant in newtons per meter and
x
x
x
is the distance the springs compress or stretch. Tractor seats are mounted on springs to absorb impact. If the springs have a spring constant of
25
25
25
,
600
600
600
newtons per meter, what is the distance, in meters, the springs must compress or stretch in order to store
8
8
8
joules of potential energy?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
000625
000625
000625
\newline
(B)
0
0
0
.
025
025
025
\newline
(C)
3200
3200
3200
\newline
(D)
102
102
102
,
400
400
400
meters
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Find the quadratic polynomial that completes the factorization.
\newline
x
3
−
64
=
(
x
−
4
)
(
_
_
_
_
_
)
x^3 - 64 = (x - 4)(\_\_\_\_\_)
x
3
−
64
=
(
x
−
4
)
(
_____
)
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Find the binomial that completes the factorization.
\newline
t
3
−
125
=
(
‾
)
(
t
2
+
5
t
+
25
)
t^3 - 125 = (\underline{\hspace{3em}})(t^2 + 5t + 25)
t
3
−
125
=
(
)
(
t
2
+
5
t
+
25
)
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Find the binomial that completes the factorization.
\newline
p
3
−
1
=
(
‾
)
(
p
2
+
p
+
1
)
p^3 - 1 = (\underline{\hspace{3cm}})(p^2 + p + 1)
p
3
−
1
=
(
)
(
p
2
+
p
+
1
)
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Find the quadratic polynomial that completes the factorization.
\newline
x
3
+
512
=
(
x
+
8
)
(
_
_
_
_
_
)
x^3 + 512 = (x + 8)(\_\_\_\_\_)
x
3
+
512
=
(
x
+
8
)
(
_____
)
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Find the binomial that completes the factorization.
\newline
x
3
+
8
=
(
‾
)
(
x
2
−
2
x
+
4
)
x^3 + 8 = (\underline{\hspace{3cm}})(x^2 - 2x + 4)
x
3
+
8
=
(
)
(
x
2
−
2
x
+
4
)
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Find the quadratic polynomial that completes the factorization.
\newline
q
3
−
125
=
(
q
−
5
)
(
_
_
_
_
_
_
)
q^3 - 125 = (q - 5)(\_\_\_\_\_\_)
q
3
−
125
=
(
q
−
5
)
(
______
)
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Find the quadratic polynomial that completes the factorization.
\newline
t
3
+
1
=
(
t
+
1
)
(
_
_
_
_
_
)
t^3 + 1 = (t + 1)(\_\_\_\_\_)
t
3
+
1
=
(
t
+
1
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
c
3
−
216
=
(
c
−
6
)
(
_
_
_
_
_
)
c^3 - 216 = (c - 6)(\_\_\_\_\_)
c
3
−
216
=
(
c
−
6
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
u
3
+
1
=
(
u
+
1
)
(
_
_
_
_
_
)
u^3 + 1 = (u + 1)(\_\_\_\_\_)
u
3
+
1
=
(
u
+
1
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
c
3
+
8
=
(
c
+
2
)
(
_
_
_
_
_
)
c^3 + 8 = (c + 2)(\_\_\_\_\_)
c
3
+
8
=
(
c
+
2
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
r
3
−
512
=
(
r
−
8
)
(
_
_
_
_
_
)
r^3 - 512 = (r - 8)(\_\_\_\_\_)
r
3
−
512
=
(
r
−
8
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
x
3
−
y
3
=
(
x
−
y
)
(
_
_
_
_
_
)
x^3 - y^3 = (x - y)(\_\_\_\_\_)
x
3
−
y
3
=
(
x
−
y
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
y
3
+
z
3
=
(
y
+
z
)
(
_
_
_
_
_
)
y^3 + z^3 = (y + z)(\_\_\_\_\_)
y
3
+
z
3
=
(
y
+
z
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
x
3
−
1
=
(
x
−
1
)
(
_
_
_
_
_
)
x^3 - 1 = (x - 1)(\_\_\_\_\_)
x
3
−
1
=
(
x
−
1
)
(
_____
)
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Find the binomial that completes the factorization.
\newline
q
3
−
r
3
=
(
‾
)
(
q
2
+
q
r
+
r
2
)
q^3 - r^3 = (\underline{\hspace{3em}})(q^2 + qr + r^2)
q
3
−
r
3
=
(
)
(
q
2
+
q
r
+
r
2
)
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Find the quadratic polynomial that completes the factorization.
\newline
w
3
+
125
=
(
w
+
5
)
(
_
_
_
_
_
)
w^3 + 125 = (w + 5)(\_\_\_\_\_)
w
3
+
125
=
(
w
+
5
)
(
_____
)
Get tutor help
Find the quadratic polynomial that completes the factorization.
\newline
q
3
+
r
3
=
(
q
+
r
)
(
_
_
_
_
_
)
q^3 + r^3 = (q + r)(\_\_\_\_\_)
q
3
+
r
3
=
(
q
+
r
)
(
_____
)
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Find the quadratic polynomial that completes the factorization.
\newline
w
3
+
8
=
(
w
+
2
)
(
_
_
_
_
_
)
w^3 + 8 = (w + 2)(\_\_\_\_\_)
w
3
+
8
=
(
w
+
2
)
(
_____
)
Get tutor help
Find the quadratic polynomial that completes the factorization.
\newline
r
3
+
s
3
=
(
r
+
s
)
(
_
_
_
_
_
)
r^3 + s^3 = (r + s)(\_\_\_\_\_)
r
3
+
s
3
=
(
r
+
s
)
(
_____
)
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4
4
4
. Determine how many REAL solutions the quadratic equation has.
\newline
2
x
2
−
x
5
+
2
=
0
2 x^{2}-x \sqrt{5}+2=0
2
x
2
−
x
5
+
2
=
0
\newline
No real solutions
\newline
One real solution
\newline
Two real solutions
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(iii)
5
+
x
y
5+x y
5
+
x
y
is a trinomial
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Determine the minimum value of
y
=
(
x
−
5
)
2
y=(x-5)^2
y
=
(
x
−
5
)
2
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40
40
40
.
a
2
−
b
2
+
2
a
+
1
a
+
1
+
b
=
\frac{a^{2}-b^{2}+2 a+1}{a+1+b}=
a
+
1
+
b
a
2
−
b
2
+
2
a
+
1
=
?
\newline
A)
a
+
3
b
+
1
a+3 b+1
a
+
3
b
+
1
\newline
B)
3
a
−
b
+
1
3 a-b+1
3
a
−
b
+
1
\newline
C)
a
−
b
+
1
a-b+1
a
−
b
+
1
\newline
D)
a
−
b
+
3
a-b+3
a
−
b
+
3
\newline
E)
a
+
b
−
1
a+b-1
a
+
b
−
1
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Combine the
4
4
4
integers to write expressions that equal the following answers.
\newline
- 3 \longdiv { 5 } - 1 5
\newline
31
31
31
.
5
×
(
−
3
)
+
15
+
(
−
9
)
=
−
9
5 \times(-3)+15+(-9)=-9
5
×
(
−
3
)
+
15
+
(
−
9
)
=
−
9
\newline
32
32
32
.
(
−
3
)
+
5
+
15
+
(
−
9
)
=
8
(-3)+5+15+(-9)=8
(
−
3
)
+
5
+
15
+
(
−
9
)
=
8
\newline
33
33
33
.
15
÷
5
−
(
−
9
)
+
(
−
3
)
=
9
15 \div 5-(-9)+(-3)=9
15
÷
5
−
(
−
9
)
+
(
−
3
)
=
9
\newline
34
34
34
.
=
−
7
=-7
=
−
7
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Find the zeros of the function
F
(
x
)
=
x
3
+
8
F(x)=x^3+8
F
(
x
)
=
x
3
+
8
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Evaluate the expression with the given replacement value.
\newline
x
2
when
x
=
−
8
x^{2} \text { when } x=-8
x
2
when
x
=
−
8
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What term should go in the box to make the statement true?
\newline
3
x
2
+
10
x
−
8
=
(
3
x
−
2
)
(
x
3x^2+10x-8=(3x-2)(x
3
x
2
+
10
x
−
8
=
(
3
x
−
2
)
(
x
+
□
)
\square)
□
)
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Complete the factoring.
\newline
x
2
+
6
x
−
40
=
(
x
−
4
)
(
□
)
x^{2}+6x-40=(x-4)(\square)
x
2
+
6
x
−
40
=
(
x
−
4
)
(
□
)
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x
2
+
(
x
+
y
)
2
=
9
x^{2}+(x+y)^{2}=9
x
2
+
(
x
+
y
)
2
=
9
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
3
x
−
7
,
3
x
−
10
,
3
x
−
13
,
...
3 x-7, \quad 3 x-10, \quad 3 x-13, \quad \text {... }
3
x
−
7
,
3
x
−
10
,
3
x
−
13
,
...
\newline
−
3
-3
−
3
\newline
17
17
17
\newline
−
17
-17
−
17
\newline
3
3
3
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a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
a^{2}-b^{2}=(a+b)(a-b)
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
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Complet the T chart of values for the Quadratic:
\newline
When you have checked your quiz and know that your T-Chart is correct, graph this Quadratic and upload it (along with the others) on the Graph Upload Assignment for points
\newline
x
=
y
2
+
4
x=y^{2}+4
x
=
y
2
+
4
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