Answer:
a) (x-2)*(x+5)*(x-3)
Step-by-step explanation:
We are given that f(x) = [tex]x^{3}-19x+30[/tex].
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) = [tex](x+5)[/tex] * ([tex]x^{2}+5x+6[/tex]).
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).
