How do you factor given that f(6)=0 and f(x)=x^3-3x^2-16x-12?

1 Answer
Sep 4, 2017

f(x)=(x-6)(x+1)(x+2)

Explanation:

"using the "color(blue)"factor theorem"

•color(white)(x)f(a)=0" if and only if "(x-a)" is a factor of "f(x)

f(6)=0rArr(x-6)" is a factor of "f(x)

f(x)=color(red)(x^2)(x-6)color(magenta)(+6x^2)-3x^2-16x-12

color(white)(f(x))=color(red)(x^2)(x-6)color(red)(+3x)(x-6)color(magenta)(+18x)-16x-12

color(white)(f(x))=color(red)(x^2)(x-6)color(red)(+3x)(x-6)color(red)(+2)(x-6)color(magenta)(+12)-12

color(white)(f(x))=color(red)(x^2)(x-6)color(red)(+3x)(x-6)color(red)(+2)(x-6)+0

rArrf(x)=(x-6)(color(red)(x^2+3x+2))

color(white)(rArrf(x))=(x-6)(x+1)(x+2)