Question

given the function $c(x) = -9(x - 2)^3(x + 6)^6(x - 4)$, its roots are enter a list of integer or decimal numbers more.. and their multiplicities are.

Explanation:

Step1: Find roots via zero factor

Set each factor equal to 0:
$x-2=0 \implies x=2$
$x+6=0 \implies x=-6$
$x-4=0 \implies x=4$

Step2: Identify multiplicities

Multiplicity = exponent of each factor:
For $x=2$: exponent is 3
For $x=-6$: exponent is 6
For $x=4$: exponent is 1

Answer:

Roots: $2, -6, 4$
Multiplicities: $3, 6, 1$