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dlinn [17]
2 years ago
9

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

Mathematics
2 answers:
nirvana33 [79]2 years ago
8 0
A. (x-2)(x+5)(x-3) is the correct answer to this question : )
Angelina_Jolie [31]2 years ago
4 0

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).

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