Question

Can you pease help me find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic devision?

thank you!

Answer 1

x^3 - 5x^2 + 6x - 30

| 1 - 5 6 - 30
|
|
5 | 5 0 30
----------------------------------------------
| 1 0 6 0 <------ the resiude is 0.

Resiude 0 means that the polynomial is divisible by x - 5, and that means the root is x = 5.

That is the only rooto because the quotient is x^2 + 6, which does not have real roots.

Answer: x = 5