Question

identify the zeros of the function and their possible multiplicities of the polynomial function. f(x) = 3x(x - 2)(x + 4) a. 0 with multiplicity 1,2 with multiplicity 2, and -4 with multiplicity 1 b. 0 with multiplicity 1,2 with multiplicity 2, and -4 with multiplicity 2 c. 0 with multiplicity 1,2 with multiplicity 1, and -4 with multiplicity 1 d. 0 with multiplicity 1,-2 with multiplicity 1, and 4 with multiplicity 1

Explanation:

Step1: Set function to 0

$3x(x-2)(x+4)=0$

Step2: Solve for each factor

$3x=0 \implies x=0$; $x-2=0 \implies x=2$; $x+4=0 \implies x=-4$

Step3: Check factor exponents

Each factor $(x-a)$ has exponent 1.

Answer:

C. 0 with multiplicity 1,2 with multiplicity 1, and -4 with multiplicity 1