Si f(3) = 0 y f( - 1) = 0, entonces la función polinomial se puede representar como ?

¡Buenas!

<img src="https://tex.z-dn.net/?f=%5Ctextrm%7BEl%20problema%20nos%20dice%20que%20se%20trata%20de%20una%20funci%5C%27on%20polinomial%7D%20%5C%5C%20%5Ctextrm%7Besto%20es%20%5C%27util%20para%20saber%20como%20tratar%20el%20problema%7D%20%5C%5C%20%5C%5C%20%5Ctextrm%7BUna%20funci%5C%27on%20polinomial%20tiene%20la%20siguiente%20forma%7D%20%5C%5C%20%5C%5C%20f%28x%29%20%3D%20a_%7B0%7Dx%5E%7Bn%7D%2Ba_%7B1%7Dx%5E%7Bn-1%7D%2Ba_%7B2%7Dx%5E%7Bn-2%7D%2Ba_%7B3%7Dx%5E%7Bn-3%7D%2B%20%5Cldots%5C%20%2B%20a_%7Bn-1%7Dx%2Ba_%7Bn%7D%3B%5C%20a_%7B0%7D%20%5Cneq%200" />

<img src="https://tex.z-dn.net/?f=%5Ctextrm%7Bentonces%20el%20problema%20nos%20dice%20que%20para%20cuando%20la%20variable%20tome%20el%7D%20%5C%5C%20%5Ctextrm%7Bvalor%20de%20%5Cboldsymbol%7B3%7D%20y%20%5Cboldsymbol%7B-1%7D%20la%20funci%5C%27on%20ser%5C%27a%200.%7D" />

<img src="https://tex.z-dn.net/?f=f%283%29%20%3D%20a_%7B0%7D%283%5E%7Bn%7D%29%2Ba_%7B1%7D%283%5E%7Bn-1%7D%29%2Ba_%7B2%7D%283%5E%7Bn-2%7D%29%2B%20%5Cldots%5C%20%2B%20a_%7Bn-1%7D%283%29%2Ba_%7Bn%7D%20%3D%200%20%5C%5C%20%5C%5C%20f%28-1%29%20%3D%20a_%7B0%7D%28-1%5E%7Bn%7D%29%2Ba_%7B1%7D%28-1%5E%7Bn-1%7D%29%2B%20%5Cldots%5C%20%2B%20a_%7Bn-1%7D%28-1%29%2Ba_%7Bn%7D%20%3D%200%20%5C%5C%20%5C%5C%20%5Ctextrm%7BEn%20ambas%20funciones%20podemos%20notar%20que%7D%5C%20%5Cboldsymbol%7Ba_%7Bn%7D%7D%5C%20%5Ctextrm%7Bno%20varia%2C%20sumado%20a%20eso%7D%20%5C%5C%20%5Ctextrm%7Bel%20valor%20de%20la%20funci%5C%27on%20se%20mantiene%20igual%3B%20podemos%20desarrollar%7D%20%5C%5C%20%5Ctextrm%7Bdistintas%20funciones%20de%20grados%20distintos%20que%20nos%20den%20ambos%20valores...%7D%20%5C%5C%20%5Ctextrm%7Bpero%20solo%20ser%5C%27a%20necesario%20un%20ejemplo.%7D" />

<img src="https://tex.z-dn.net/?f=%20%5Ctextrm%7BFUNCI%5C%27ON%20POLINOMIAL%5C%20DE%5C%20SEGUNDO%20GRADO%7D%20%5C%5C%20%5C%5C%20f%28x%29%3Dax%5E%7B2%7D%2Bbx%2Bc%3D0%20%5C%5C%20%5C%5C%20%5Cboxed%7Bx_%7B1%7D%20%3D%203%7D%5C%20%5C%20%5Cboxed%7B%20x_%7B2%7D%20%3D%20-1%7D%20%5C%5C%20%5C%5C%20%5Cboldsymbol%7Bx_%7B1%7D%7D%5C%20%5Ctextrm%7By%7D%5C%20%5Cboldsymbol%7Bx_%7B2%7D%7D%5C%20%5Ctextrm%7Bra%5C%27ices%20de%20la%20ecuaci%5C%27on%7D%20%5C%5C%20%5C%5C%20%5Ctextrm%7BUna%20ecuaci%5C%27on%20de%20segundo%20grado%20se%20puede%20formar%20con%20sus%20ra%5C%27ices%20de%20la%7D%20%5C%5C%20%5Ctextrm%7Bsiguiente%20manera.%7D%20%5C%5C%20%5C%5C%20x%5E%7B2%7D-%28x_%7B1%7D%2Bx_%7B2%7D%29x%2Bx_%7B1%7Dx_%7B2%7D%20%3D%200%20%5C%5C%20%5C%5C%20x%5E%7B2%7D-%283-1%29x%2B3%28-1%29%3D0%20%5C%5C%20%5C%5C%20x%5E%7B2%7D-2x-3%3D0%20" />

RESPUESTA

<img src="https://tex.z-dn.net/?f=%5Cboxed%7Bf%28x%29%20%3D%20x%5E%7B2%7D-2x-3%20%7D" />.