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Sagot :
The polynomials in factored form are listed below:
- f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716)
- f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
- f(x) = (x + 3) · (x - 5) · (x - 1)
- f(x) = (x - 4) · (x - 3) · (x - 1) · x
How to factor polynomials
In this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:
[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex] (1)
Where:
- [tex]c_{i}[/tex] - [tex]i[/tex]-th Coefficient
- [tex]r_{i}[/tex] - [tex]i[/tex]-th Root
Regarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:
Polynomial 1 ([tex]f(x) = x^{3}-4\cdot x +16[/tex])
f(x) = (x - 4) · (x - 3) · (x - 1) · x
Polynomial 2 ([tex]f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40[/tex])
f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
Polynomial 3 ([tex]f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15[/tex])
f(x) = (x + 3) · (x - 5) · (x - 1)
Polynomial 4 ([tex]f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x[/tex])
f(x) = (x - 4) · (x - 3) · (x - 1) · x
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016
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