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Sagot :
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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