Respuesta :
Answer:
A. (x – 2)(x + 5)(x – 3) on edg
Step-by-step explanation:
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When a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial. The factors of x³-5x+6 are (x+5)(x-2)(x-3).
What is the Remainder theorem?
According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.
Since f(–5) = 0, therefore, (x+5) is a factor of the polynomial f(x).
[tex]\dfrac{x^3-19x+30}{x+5} = x^2-5x+6[/tex]
Now, x² -5x + 6 can be factorised as,
x² - 5x + 6
x² - 2x - 3x + 6
x(x-2) -3 (x-2)
(x-2)(x-3)
Hence, the factors of x³-5x+6 are (x+5)(x-2)(x-3).
Learn more about the Remainder Theorem:
https://brainly.com/question/13264870
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