Find the equation of the polynomial

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To find the polynomial of degree 4 with zeros at -2, 2, 1, and 1, start by using the fact that the polynomial can be expressed as a product of its factors. The factors corresponding to the given zeros are (x + 2), (x - 2), and (x - 1)², since 1 is a repeated root. The polynomial can be constructed as P(x) = (x + 2)(x - 2)(x - 1)². Expanding this product will yield the final polynomial equation with a leading coefficient of 1. The key is to multiply the factors correctly to find the complete polynomial expression.
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Homework Statement


Find the equation of the polynomial of degree 4 with zero's at -2, 2, 1, 1 and a leading coefficient of 1.


Homework Equations


?


The Attempt at a Solution


I don't know how to attack this one, I'm sure if I could see how to do it I could do it myself byt my head isn't working right now. All I can gather from that information is the first bit is x ^ 4 - Which isn't much. I'm thinking I have to substitue the values for zero into an equation and solve simultaneously? Can anyone help?
 
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Noir said:
Find the equation of the polynomial of degree 4 with zero's at -2, 2, 1, 1 and a leading coefficient of 1.

Hi Noir! :smile:

Hint: factors :wink:
 

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