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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 :

Facundo3141592idn

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

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