Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

After factoring the following polynomial completely, use the Fundamental-Theorem of Algebra
to determine the number of roots of the polynomial. Then, determine which of the factors has a
multiplicity of 3 and compare it to the Code Breaker Guide to find the fifth piece of the code.
(x + 7)(x - 2)²(x2 – 4)(x + 1)^*

Sagot :

MrRoyal

The factor that has a multiplicity of 3 is x - 2, and the polynomial has 7 roots.

The polynomial

The polynomial is given as:

[tex]P(x) = (x + 7)(x - 2)\²(x^2 - 4)(x + 1)^2[/tex]

Express 4 as 2^2. So, the polynomial becomes

[tex]P(x) = (x + 7)(x - 2)\²(x^2 - 2^2)(x + 1)^2[/tex]

Apply the difference of two squares on (x^2 - 2^2).

So, we have:

[tex]P(x) = (x + 7)(x - 2)\²(x - 2)(x + 2)(x + 1)^2[/tex]

Group the common factors

[tex]P(x) = (x + 7)(x - 2)^3(x + 2)(x + 1)^2[/tex]

Multiplicity

For a factor to have a multiplicity of 3, it means that the exponent (i.e. power) is 3.

This means that x - 2 has a multiplicity of 3.

The number of roots

Next, we add the multiplicities of each factor, to get the number of roots.

[tex]n = 1 + 3 + 1 + 2[/tex]

[tex]n = 7[/tex]

Hence, the polynomial has 7 roots

Read more about polynomials at:

https://brainly.com/question/2833285

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.