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Algebra 2
Write a polynomial from its roots
We want to find the zeros of this polynomial:
\newline
p
(
x
)
=
x
(
2
x
+
3
)
(
x
−
1
)
(
x
+
2
)
p(x)=x(2 x+3)(x-1)(x+2)
p
(
x
)
=
x
(
2
x
+
3
)
(
x
−
1
)
(
x
+
2
)
\newline
Plot all the zeros (
x
x
x
-intercepts) of the polynomial in the interactive graph.
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2
2
2
. Find the equation of the exponential given
(
2
,
2
)
(2,2)
(
2
,
2
)
and
(
3
,
4
)
(3,4)
(
3
,
4
)
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Write a polynomial of least degree with roots
7
7
7
and
−
5
-5
−
5
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
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Write a polynomial of least degree with roots
3
3
3
and
9
9
9
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Write a polynomial of least degree with roots
−
8
-8
−
8
and
9
9
9
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Write a polynomial of least degree with roots
8
8
8
and
−
7
-7
−
7
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
Get tutor help
Write a polynomial of least degree with roots
7
7
7
and
−
8
-8
−
8
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
Get tutor help
Write a polynomial of least degree with roots
8
8
8
and
−
5
-5
−
5
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Write a polynomial of least degree with roots
2
2
2
and
−
3
-3
−
3
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Write a polynomial of least degree with roots
6
6
6
and
−
6
-6
−
6
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
Get tutor help
Write a polynomial of least degree with roots
3
3
3
and
−
6
-6
−
6
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Write a polynomial of least degree with roots
8
8
8
and
−
2
-2
−
2
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Write a polynomial of least degree with roots
2
2
2
and
−
4
-4
−
4
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
Get tutor help
Write a polynomial of least degree with roots
6
6
6
and
−
4
-4
−
4
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
Get tutor help
Write a polynomial of least degree with roots
−
9
-9
−
9
and
−
8
-8
−
8
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
Get tutor help
Write a polynomial of least degree with roots
9
9
9
and
−
6
-6
−
6
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
Get tutor help
Write a polynomial of least degree with roots
9
9
9
and
−
7
-7
−
7
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
______
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Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
3
(
9
x
−
7
)
−
1
=
4
x
+
6
(
−
x
+
7
)
3(9 x-7)-1=4 x+6(-x+7)
3
(
9
x
−
7
)
−
1
=
4
x
+
6
(
−
x
+
7
)
\newline
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Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
4
+
6
(
−
8
x
+
8
)
=
4
(
9
x
−
5
)
+
5
4+6(-8 x+8)=4(9 x-5)+5
4
+
6
(
−
8
x
+
8
)
=
4
(
9
x
−
5
)
+
5
\newline
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8
−
4
(
−
x
+
5
)
8-4(-x+5)
8
−
4
(
−
x
+
5
)
\newline
Which of the following is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
x
−
12
4 x-12
4
x
−
12
\newline
(B)
−
4
x
−
12
-4 x-12
−
4
x
−
12
\newline
(C)
4
x
+
13
4 x+13
4
x
+
13
\newline
(D)
4
x
+
5
4 x+5
4
x
+
5
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2
2
2
. Write an inequality for which
3
,
−
4
,
0
3,-4,0
3
,
−
4
,
0
, and
2
2
2
,
300
300
300
are salutions.
\newline
b. How many total solutions are there to your inequality?
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Three points on the graph of the function
f
(
x
)
f(x)
f
(
x
)
are
{
(
0
,
3
)
,
(
1
,
9
)
,
(
2
,
27
)
}
\{(0,3),(1,9),(2,27)\}
{(
0
,
3
)
,
(
1
,
9
)
,
(
2
,
27
)}
. Which equation represents
f
(
x
)
f(x)
f
(
x
)
?
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The side of a square in terms of
x
\mathrm{x}
x
is
4
x
+
7
4 x+7
4
x
+
7
.
\newline
a. Write a polynomial that represents the perimeter of the square.
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Find the polynomial function
f
f
f
with real coefficients that has the given degree, zeros, and solution point.
\newline
Degree
Zeros
Solution Point
3
−
9
,
1
+
3
i
f
(
−
2
)
=
84
\begin{array}{ccc} \text { Degree } & \text { Zeros } & \text { Solution Point } \\ 3 & -9,1+\sqrt{3} i & f(-2)=84 \end{array}
Degree
3
Zeros
−
9
,
1
+
3
i
Solution Point
f
(
−
2
)
=
84
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Write a polynomial
f
(
x
)
f(x)
f
(
x
)
that satisfies the given conditions. Polynomial of lowest degree with zeros of
5
3
\frac{5}{3}
3
5
(multiplicity
2
2
2
) and
−
2
3
-\frac{2}{3}
−
3
2
(multiplicity
1
1
1
) and with
f
(
0
)
=
−
100
f(0)=-100
f
(
0
)
=
−
100
.
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Write a polynomial of least degree with real coefficients and with the root
1
−
6
i
1-6i
1
−
6
i
.
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Let
h
(
x
)
=
x
+
12
−
3
x
+
3
h(x)=\frac{\sqrt{x+12}-3}{x+3}
h
(
x
)
=
x
+
3
x
+
12
−
3
when
x
≠
−
3
x \neq-3
x
=
−
3
.
\newline
h
h
h
is continuous for all
x
>
−
12
x>-12
x
>
−
12
.
\newline
Find
h
(
−
3
)
h(-3)
h
(
−
3
)
.
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
9
-\frac{1}{9}
−
9
1
\newline
(B)
1
9
\frac{1}{9}
9
1
\newline
(c)
−
1
6
-\frac{1}{6}
−
6
1
\newline
(D)
1
6
\frac{1}{6}
6
1
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Write a polynomial of least degree with roots
6
6
6
and
−
5
-5
−
5
.
\newline
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
\newline
______
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