Consider the function F (x) = x^3-6x^2+9x. What are the x-intercepts of F (x) ? write the soltuin (s) as ordered pairs.

(x^3-6x+9x) / x = x (x^2+6x+9)

(x) (x^2+6x+9) x-3=0 x=0

(x) (x-3) (x-3) + 3 + 3

(3,0) (0,0)

X intercepts are the roots (remember that y=0 at x intercepts)

for roots r1 and r2, the factors are (x-r1) and (x-r2)

factor

f (x) = x^3-6x^2+9x

factour out x

f (x) = (x) (x^2-6x+9)

factor

f (x) = (x) (x-3) (x-3)

f (x) = (x-0) (x-3) (x-3)

the x intercepts are at x=0, and at x=3

solutions are

(0,0) and (3,0)