Question

Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1,given that f(0)=60.

f(x)=

Answer 1

Up to multiples, if you're given the roots you can write the polynomial by multiplying several parenthesis in the form

`(x-x_0)`

where
`x_0` is a root. So, in your case, you have

`f(x) = a(x+6)(x+5)(x+1)`

We can fix the parameter a by imposing f(0)=60:

`f(0)=a(0+6)(0+5)(0+1)=30a=60\iff a=2`

So, your polynomial is

`f(x) = 2(x+6)(x+5)(x+1)=2x^3+24x^2+82x+60`