Question

HELP

Answer 1

Answer:

$(x+6)$ and $(x-3-\sqrt{5})$

Step-by-step explanation:

We have been given that a polynomial function f(x) has roots $3+\sqrt{5}$ and $-6$. 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:

$x=3+\sqrt{5}$ and $x=-6$.

To find the factors of our given function, we will bring the expression on right side to left side as:

$x-3-\sqrt{5}=3+\sqrt{5}-3-\sqrt{5}$

$x-3-\sqrt{5}=0$

Similarly, we will get:

$x+6=-6+6$

$x+6=0$

Therefore, $(x+6)$ and $(x-3-\sqrt{5})$ are factors of our given function.

 

Answer 2

If r is a zero of f(x), x-r is a factor of f(x)

Since -6 is a zero, x+6 is a factor

Since 3+√5 is a zero, x-3-√5 is a factor