If a polynomial function f(x) has roots 3+sqrt(5) and -6, what must be a factor of f(x)

The two factors of the given polynomial f(x) are (x - 3 -√5) and (x +6) .

Step-by-step explanation:

Here, the roots of the given polynomial f(x)  are

Root 1  =  3 + √5

and  Root 2   =  (-6)

Now,as we know that if x  = a is the root of the any given polynomial p(x), then the expression (x-a) is the FACTOR of the polynomial p(x).

Now, here root 1 : x  = 3 + √5

So, x  - (3 + √5 ) is the FACTOR of the f(x)

or, ( x - 3 -√5) is the   first factor of f(x).

Also, here root 2 : x  = (-6)

So, x  - (-6 )   = x + 6   is the FACTOR of the f(x)

or, ( x +6 ) is the second factor of f(x).

Hence, the two factors of the given polynomial f(x)

are ( x - 3 -√5) and  ( x +6 ) .

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step-by-step explanation:

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