List each zero of the polynomial, together with its multiplicity:

Given: [tex]P(x) = -12(x - 3)^3(x - 7)^5(x - 5)^7(x - 8)^9[/tex]

a) [tex]x = 3[/tex], multiplicity 3; [tex]x = 7[/tex], multiplicity 5; [tex]x = 5[/tex], multiplicity 7; [tex]x = 8[/tex], multiplicity 9

b) [tex]x = 3[/tex], multiplicity 5; [tex]x = 7[/tex], multiplicity 7; [tex]x = 5[/tex], multiplicity 9; [tex]x = 8[/tex], multiplicity 3

c) [tex]x = 3[/tex], multiplicity 9; [tex]x = 7[/tex], multiplicity 7; [tex]x = 5[/tex], multiplicity 5; [tex]x = 8[/tex], multiplicity 3

d) [tex]x = 3[/tex], multiplicity 7; [tex]x = 7[/tex], multiplicity 3; [tex]x = 5[/tex], multiplicity 9; [tex]x = 8[/tex], multiplicity 5

The polynomial given is P(x) = -12(x - 3)3(x - 7)5(x - 5)7(x - 8)9. The zeroes of a polynomial are obtained by setting the polynomial equal to zero and solving for x. These zeroes can be easily identified in factorized form of polynomials and the exponents of each factor determine the multiplicity of the corresponding zeroes. In the polynomial given:

x = 3 is a zero with multiplicity of 3 as it is denoted by (x - 3)3
x = 7 is a zero with multiplicity of 5 as denoted by (x - 7)5
x = 5 is a zero with multiplicity of 7 as denoted by (x - 5)7
x = 8 is a zero with multiplicity of 9 as denoted by (x - 8)9

So, the correct answer is option A: x = 3, multiplicity 3; x = 7, multiplicity 5; x = 5, multiplicity 7; x = 8, multiplicity 9.

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