If f(–5) = 0, what are all the factors of the function f(x)=x^3-19x+30? use the remainder theorem.

a. (x – 2)(x + 5)(x – 3)
b. (x + 2)(x – 5)(x + 3)
c. (x – 2)(x + 5)
d. (x + 2)(x – 5)

a) (x-2)*(x+5)*(x-3)

Step-by-step explanation:

We are given that f(x) = .

Now, f(-5)=0 i.e. (x+5) is a factor of f(x),

We need to find the other two factors.

So, using Remainder Theorem, we get that f(x) is simplified into f(x) = * ().

Now, after solving the quadratic equations, we get that,

f(x) = (x+5)*(x-2)*(x-3).

Hence, a) (x-2)(x+5)(x-3) are the factors of f(x).

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step-by-step explanation: