Express each cubic function below in terms of linear factors. a) f (x) = x³-6x²-27xb) f (x) = x³-16x²c) f (x) = x³+16x²

a) x (x-9) (x+3)

b) x (x+4) (x-4)

c) (x) (x) (x + 16)

Step-by-step explanation:

We're going to equal the functions to zero and find their roots by factorizing:

a) f (x) = x³-6x²-27x

x³-6x²-27x = 0

x (x²-6x-27) = 0

⇒x (x-9) (x+3)

b) f (x) = x³-16x

x³-16x = 0

x (x²-16) = 0

⇒x (x+4) (x-4)

c) f (x) = x³+16x²

x³ + 16x² = 0

x² (x + 16)

⇒ (x) (x) (x + 16)