Helpppp meeeeee please i a test and i need the answer right now please!!!!!
Suppose that a polynomial function p can be factored into seven factors: (x-3), (x+1) and 5 factors of (x-2). What are its zeros with multiplicity, and what is the degree of the polyno-mial? Explain how you know. (You won't get full grade if you don not explain your answer.) (10)

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Respuesta :

bennype90 bennype90 · Answer 1 · 2020-10-02T17:53:28+02:00

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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