Answer to Question #43001 in Calculus for shasha

Question

Find the zeros of the polynomial function and state the multiplicity of each.

f(x) = 3(x + 9)2(x - 9)3

4, multiplicity 1; -9, multiplicity 3; 9, multiplicity 3

4, multiplicity 1; 9, multiplicity 1; -9, multiplicity 1

-9, multiplicity 3; 9, multiplicity 2

-9, multiplicity 2; 9, multiplicity 3


help me please

Answer 1

The product equals zero only if at least one of the multipliers equal zero. Therefrom we get
(x+9)² = 0 or (x-9)³ = 0
x = -9 with multiplicity 2 and x=9 with multiplicity 3.