The polynomials in <em>factored</em> form are listed below:
- <em>f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716)</em>
- <em>f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)</em>
- <em>f(x) = (x + 3) · (x - 5) · (x - 1)</em>
- <em>f(x) = (x - 4) · (x - 3) · (x - 1) · x</em>
<h3>How to factor polynomials</h3>
In this question we must factor polynomials as there are both <em>numerical</em> and <em>analytical</em> methods. Mathematically speaking, factoring polynomials is represented by the following formula:
,
(1)
Where:
-
-th Coefficient
-
-th Root
Regarding <em>fourth order</em> polynomials we can solve them by Ferrari's method and <em>third order</em> polynomials by Descartes' method. Then, the solutions of each polynomials are given below:
<h3>Polynomial 1 (

)</h3>
<em>f(x) = (x - 4) · (x - 3) · (x - 1) · x</em>
<h3>Polynomial 2 (

)</h3>
<em>f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)</em>
<h3>Polynomial 3 (

)</h3>
<em>f(x) = (x + 3) · (x - 5) · (x - 1)</em>
<h3>Polynomial 4 (

)</h3>
<em>f(x) = (x - 4) · (x - 3) · (x - 1) · x</em>
To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/17822016