Answer:
The correct option is D) 5, 4, 3
Step-by-step explanation:
Consider the provided function.
[tex]f(x) = x^3 -12x^2 + 47x - 60[/tex]
It is given that one factor is (x-5) and we need to find the zeros of the function.
That means x-5 will completely divide the provided polynomial.
[tex]\frac{x^3 -12x^2 + 47x - 60}{x-5}[/tex]
The long division is shown in figure below.
[tex]\frac{x^3-12x^2+47x-60}{x-3}=x^2-7x+12[/tex]
Simplify the expression [tex]x^2-7x+12[/tex]
[tex]x^2-4x-3x+12[/tex]
[tex]x(x-4)-3(x-4)[/tex]
[tex](x-4)(x-3)[/tex]
[tex](x-4)(x-3)[/tex]
Therefore, the required polynomial can be written as: [tex]f(x)=(x-3)(x-4)(x-5)[/tex]
Now find the zeros by substituting f(x)=0.
[tex](x-3)(x-4)(x-5)=0[/tex]
[tex]x-3=0\ or\ x-4=0\ or\ x-5=0[/tex]
[tex]x=3\ or\ x=4\ or\ x=5[/tex]
Hence, the correct option is D) 5, 4, 3
