if (f(-2)=0), what are all the factors of the function (f(x)=x^{3}-2x^{2}-68x - 120)? use the remainder…

if (f(-2)=0), what are all the factors of the function (f(x)=x^{3}-2x^{2}-68x - 120)? use the remainder theorem.\n((x + 2)(x + 60)\n(x - 2)(x - 60)\n(x - 10)(x + 2)(x + 6)\n(x + 10)(x - 2)(x - 6))

if (f(-2)=0), what are all the factors of the function (f(x)=x^{3}-2x^{2}-68x - 120)? use the remainder theorem.\n((x + 2)(x + 60)\n(x - 2)(x - 60)\n(x - 10)(x + 2)(x + 6)\n(x + 10)(x - 2)(x - 6))

Answer

Explanation:

Step1: Aplicar el Teorema del Resto

Dado que (f(- 2)=0), entonces ((x + 2)) es un factor de (f(x)=x^{3}-2x^{2}-68x - 120).

Step2: Realizar la división polinómica

Dividimos (x^{3}-2x^{2}-68x - 120) entre (x + 2) usando la división sintética o larga. [ \begin{align*} \frac{x^{3}-2x^{2}-68x - 120}{x + 2}&=x^{2}-4x-60 \end{align*} ]

Step3: Factorizar el polinomio resultante

Factorizamos (x^{2}-4x - 60). Buscamos dos números que sumen (-4) y que multipliquen (-60). Son (-10) y (6). Entonces (x^{2}-4x - 60=(x - 10)(x+6)).

Step4: Escribir todos los factores

Los factores de (f(x)) son ((x + 2)(x - 10)(x + 6)).

Answer:

C. ((x - 10)(x + 2)(x + 6))