Which expression defines function h?

Question

asked Nov 24, 2022 27.3k views

1 Answer

Liuyong · Answer 1 · 2022-11-30T09:53:21+0000

Answer:

h(x) = ((f)/(g))(x)

Explanation:

Given

f(x) = 3x^3 + 9x^2 -12x

g(x) = x - 1

h(x) = 3x^2 + 12x

Required

What defines h(x)

Looking at the degree of f(x), g(x) and h(x), we have:

h(x) = ((f)/(g))(x)

See proof

h(x) = ((f)/(g))(x)

This gives:

h(x) = (f(x))/(g(x))

h(x) = (3x^3 + 9x^2 -12x)/(x - 1)

Factorize

$h(x) = ((3x^2 + 12x)(x - 1))/(x - 1)\\$

h(x) = 3x^2 + 12x