Respuesta :
Answer:
[tex](x+6)[/tex] and [tex](x-3-\sqrt{5})[/tex]
Step-by-step explanation:
We have been given that a polynomial function f(x) has roots [tex]3+\sqrt{5}[/tex] and [tex]-6[/tex]. We are asked to find the factor of f(x).
We know that a root of function is a point for which a given function equals zero.
We can write roots of our function as:
[tex]x=3+\sqrt{5}[/tex] and [tex]x=-6[/tex].
To find the factors of our given function, we will bring the expression on right side to left side as:
[tex]x-3-\sqrt{5}=3+\sqrt{5}-3-\sqrt{5}[/tex]
[tex]x-3-\sqrt{5}=0[/tex]
Similarly, we will get:
[tex]x+6=-6+6[/tex]
[tex]x+6=0[/tex]
Therefore, [tex](x+6)[/tex] and [tex](x-3-\sqrt{5})[/tex] are factors of our given function.
