"using the "color(blue)"factor theorem"using the factor theorem
•color(white)(x)f(a)=0" if and only if "(x-a)" is a factor of "f(x)∙xf(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(6)=0⇒(x−6) is a factor of f(x)
f(x)=color(red)(x^2)(x-6)color(magenta)(+6x^2)-3x^2-16x-12f(x)=x2(x−6)+6x2−3x2−16x−12
color(white)(f(x))=color(red)(x^2)(x-6)color(red)(+3x)(x-6)color(magenta)(+18x)-16x-12f(x)=x2(x−6)+3x(x−6)+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)-12f(x)=x2(x−6)+3x(x−6)+2(x−6)+12−12
color(white)(f(x))=color(red)(x^2)(x-6)color(red)(+3x)(x-6)color(red)(+2)(x-6)+0f(x)=x2(x−6)+3x(x−6)+2(x−6)+0
rArrf(x)=(x-6)(color(red)(x^2+3x+2))⇒f(x)=(x−6)(x2+3x+2)
color(white)(rArrf(x))=(x-6)(x+1)(x+2)⇒f(x)=(x−6)(x+1)(x+2)
