Question

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

Answer 1

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

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

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

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)