Question

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)

Answer 1

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

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).