Question

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

Answer 1

A. (x-2)(x+5)(x-3) is the correct answer to this question : )

Answer 2

Answer:

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

Step-by-step explanation:

We are given that f(x) = $x^{3}-19x+30$.

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) = $(x+5)$ * ($x^{2}+5x+6$).

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).