Question

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.

Answer 1

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)

Answer 2

(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)