Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Which polynomial function f(x) has a leading coefficient of 1, roots –5, 3, and 6 with multiplicity 1, and root –2 with multiplicity 3?

f(x) = 3(x + 2)(x + 5)(x – 3)(x – 6)

f(x) = 3(x – 2)(x – 5)(x + 3)(x + 6)

f(x) = (x + 2)(x + 2)(x + 2)(x + 5)(x – 3)(x – 6)

f(x) = (x – 2)(x – 2)(x – 2)(x – 5)(x + 3)(x + 6)



Its C

Sagot :

facundo3141592

The polynomial is:

[tex]p(x) = 1*(x + 5)*(x - 3)*(x - 6)*(x + 2)*(x + 2)*(x + 2)[/tex]

Third option is the correct one.

How to identify the correct polynomial?

A polynomial of degree n, with leading coefficients a and known roots is:

[tex]P(x) = a*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]

If the leading coefficient is 1, then:

a = 1

And the roots are:

-5, 3, and 6 with a multiplicity of 1 (so these appear only one time).

-2 with a multiplicity of 3 (so that root appears 3 times).

Then the polynomial is:

[tex]p(x) = 1*(x + 5)*(x - 3)*(x - 6)*(x + 2)*(x + 2)*(x + 2)[/tex]

This is the third option, so that is the correct option.

If you want to learn more about polynomials:

https://brainly.com/question/4142886

#SPJ1

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.