# 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) = ax^{3} + bx^{2} + 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) = x^{5} + 2x^{4} - 18x^{3} - 4x^{2} + 49x - 30

9) ** FACTOR :** f (x) = 6x^{4} - 7x^{3} - 73x^{2} + 14x + 24

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

10) f (x) = x^{4} + 2x^{3} - 10x^{2} - 14x + 21

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