Question

Which of the following is a polynomial with roots 4, −5, and 7?

Answer 1

A) f(x)=x^3-6x^2-27x+140
B) f(x)=x^3-6x^2-20x+27
C) f(x)=x^3-20x^2-27x+35
D) f(x)=x^3-20x^2-35x+140

Answer 2

There's a simple way to do this, subsitute the roots for x
If it works out to be zero then it is a root
If it isn't zero it isn't a root

Answer 3

uhh yeah i dont get it

Answer 4

So I'll work out an example of what I'm doing for you
Let's try option A first
Substituting 4 for A gets you
\[4^3-6(4^2)-27(4)+140\]
Solving that gets you 0
So 4 is a root of this function, but that's not it you have to test -5 and 7 too
And IF it doesn't work for either one of them then A isn't the right answer