Question

Find a polynomial f(x) of degree 3 that has the following zeros:
-9,2,0
Leave your answer in factored form.

Answer 1

If a 3rd degree polynomial has three known roots x1,x2,x3, then the factored form is:
a(x-x1)(x-x2)(x-x3)=0
where a is an arbitrary constant.

Answer 2

So in this case, x(x+9)(x-2) ?

Answer 3

remember, zeros mean when x= -9 , x= 2 and x=0 then the polynomial is 0
if you rearrange these 3 equations you get
x+9=0
x-2=0
x=0
when you multiply them together you get
x(x-2)(x+9) = (obviously) 0
you could also multiply by some number a, and it will still be 0
a x (x-2) (x+9) = 0

Answer 4

for this question, leave a=1 for the simplest form. But you could pick any a you want (except a=0)

Answer 5

Thanks for the help.