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Finding Zeros of Polynomials

Give a possible factorization of the following polynomials. Do NOT multiply out the factors!

4) Sketch a Graph of a polynomial with the given zeros and corresponding multiplicities.
(note: the graph is not unique )

x = -5, of multiplicity 2
x
= -1, of multiplicity 1
x = 2, of multiplicity 3
x
= 4, of multiplicity 2

5) Find the zeros of the following polyno mial function and state the multiplicity of each zero.

f (x) = x (x - 1)2 (2x + 1) (x + 4)3

6) Find a polynomial function of degree 3 with the given zeros.
Write your answer in the form: f (x) = ax3 + bx2 + cx + d
x = -2 , x = - 1 , x = 2

7) Find a polynomial function ( factored form ) of degree 3
which has the corresponding table of values to the right .

x y
4
3
2
1
0
-1
-2
-3
-4
18
0
-4
0
6
8
0
-24
-70

Factor the following polynomial functions completely.
Exact answers only!!! No Decimal approximations allowed!

8) FACTOR : f (x) = x5 + 2x4 - 18x3 - 4x2 + 49x - 30

9) FACTOR : f (x) = 6x4 - 7x3 - 73x2 + 14x + 24

List the real zeros of the following polynomial. Exact answers only!!! No Decimal approx.

10) f (x) = x4 + 2x3 - 10x2 - 14x + 21

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