The polynomial f(x) has degree 3. Choose each statement that could describe all the zeros of f.

Question

-one zero with multiplicity 3

-one zero with multiplicity 4

-one zero with multiplicity 5

-one zero with multiplicity 1 and one zero with multiplicity 2

-one zero with multiplicity 1 and one zero with multiplicity 3

-one zero with multiplicity 2 and two zeros with multiplicity 1

-one zero with multiplicity 2 and three zeros with multiplicity 1

-Two zeros with multiplicity 2

-Two zero with multiplicity 2 and two zeros with multiplicity 1

-Two zero with multiplicity 2 and three zeros with multiplicity 1

-Two zero with multiplicity 1

-Three zeros with multiplicity 1

-Four zeros with multiplicity 1

-Five zeros with multiplicity 1

Answer 1

degree 3 has 3 zeroes, and never 4 or 5 in any sense

either one of 3 possibilities

1 zero with multiplicity 2 and 1 with multiplicity 1 (example x(x-2)^2 or x^3 -4x^2 + 4, which has zeroes of +2,+2 and 0) or

1 zero with multiplicity 3 (example x^3 which has zeroes of 0,0, and 0

3 zeroes each with multiplicity 1 (example x^3+9 which has factors (x+3)(x^2-3x+9) setting each factor=0 and solving for x gives zeroes of -3, 1.5+1.5sqr3, 1.5-1.5sqr3, one real and 2 imaginary zeroes)

that's the 1st, 4th and `12th choices