abebitsftdalom
Answered

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

Verified Answer :

Hagrid

The right answer for the question that is being asked and shown above is that: "A (x – 2)(x + 5)(x – 3)." If f(–5) = 0, the factors of the function f(x) = x^3 - 19x + 30 is A (x – 2)(x + 5)(x – 3), using the Remainder Theorem

frika

If f(-5)=0, then x+5 is first factor of given polynomial.

1. Divide polynomial \(x^3 - 19x + 30\) by x+5:

\(x^3 - 19x + 30=(x+5)(x^2-5x+6)\).

2. Factor the trinomial \(x^2-5x+6\):

\(D=(-5)^2-4\cdot 6=25-24=1,\ \sqrt{D}=1,\\ \\ x_1=\dfrac{5-1}{2}=2, \ x_2=\dfrac{5+1}{2}=3,\\ \\
x^2-5x+6=(x-2)(x-3)\).

3. Then

\(x^3 - 19x + 30=(x+5)(x-2)(x-3)\).

Answer: correct choice is A.

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