Answer:
Step-by-step explanation:
p
(
x
)
=
(
x
−
3
)
(
x
+
1
) (x
−
2
) (
x
-
2
) (
x
−
2
) (
x
−
2
) (
x
−
2
)
The multiplicity of an equation is how many times a zero repeats.
p
(
x
) =
(
x
−
3
) x +
1
) (
x
−
2
) 5
In the equation, zero 3 has multiplicity 1, zero -1 has multiplicity 1, and zero 2 has multiplicity 5.
The degree of the whole polynomial is the highest degree out of every term.
So first you have to expand:
p
(
x
)
=
(
x 3
) (
x
+
1
) (
x
−
2
) (
x
−
2
) (
x
−
2
) (
x
−
2
) (
x
−2
)
p
(
x
)
=
(
x
2
+
x
−
3
x
−
3
)
(
x
2
−
4
x
+
4
)
(
x
2
−
4
x
+
4
)
(
x
−
2
)
p
(
x
)
=
(
x
2
−
2
x
−3
)
(
x
2
4
+
4
)
(x
3
−
6
x
2
+
12
x
−
8
)
p
(
x
)
=
(
x
4
6
x
3
+
9
x
2
+
4
x
−12
)
(
x
3
−
6
x
2
+
12
x
−
8
)
p(x
)
= x 7
−
12
x
6
+
57
x
5
−
130
x
4
+
120
x
3
+
48
x
2−
176
x
+96
So the degree of
p
(
x
)
=
(
x
−
3
)
(
x
+
1
)
(
x
2
)
(
x
−
2
)
(
x
−
2
)
(
x
−2
)
(
x-
2
) is 7.
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