Find all the zeroes of the polynomial function f(x)=x^3 -5x^2+6x -30. If you use synthetic division, show all three lines of numbers.

Question

Find all the zeroes of the polynomial function


`f(x)=x^3 -5x^2+6x -30.` If you use synthetic division, show all three lines of numbers.

Answer 1

(x -5)(x² + 6)

Explanation:

f(x) = x³ - 5x² + 6x - 30

Synthetic division:

5 1 -5 6 -30

0 5 0 30

1 0 6 0

(x - 5) is a factor

f(x) = x³ - 5x² + 6x - 30 = (x -5)(x² + 6)