Find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30.

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

You can use synthetic division for this one, but it can also factor by grouping.

x²(x-5)+6(x-5)

(x²+6)(x-5) = 0 and now solve

x²+6=0 Subtract 6 from both sides

x²=-6 Square root of both sides, since this is a negative number, you would have an i

x= ±i√6

x-5=0 Add 5 to both sides

x=5