"given the zeros of a polynomial say"given the zeros of a polynomial say
x=a,x=b" and "x=cx=a,x=b and x=c
"then the factors are "(x-a),(x-b)" and "(x-c)then the factors are (x−a),(x−b) and (x−c)
"the polynomial is the product of the factors"the polynomial is the product of the factors
rArrp(x)=k(x-a)(x-b)(x-c)larrcolor(blue)"k is a multiplier"⇒p(x)=k(x−a)(x−b)(x−c)←k is a multiplier
"here "x=-3,x=0,x=4larrcolor(blue)"zeros"here x=−3,x=0,x=4←zeros
rArr(x+3),(x-0)" and "(x-4)" are the factors"⇒(x+3),(x−0) and (x−4) are the factors
"letting "k=1letting k=1
p(x)=x(x+3)(x-4)p(x)=x(x+3)(x−4)
color(white)(p(x))=x(x^2-x-12)p(x)=x(x2−x−12)
color(white)(p(x))=x^3-x^2-12xlarrcolor(blue)"is a possible polynomial"p(x)=x3−x2−12x←is a possible polynomial
