Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Factor each completely.one zero has been given

f(x)=x^3-4x+16;-2

F(x) = X^4+ 2x^-13x^2 -10x + 40;2

F(x)=x^3-3x^2-13x+15;-3

F(x)=x^4-8x^3+19x^2-12x;3

Sagot :

xero099

The polynomials in factored form are listed below:

  1. f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716)
  2. f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
  3. f(x) = (x + 3) · (x - 5) · (x - 1)
  4. 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

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.