Question

Consider the functions k(x) = x + 1, m(x) = x - 4, n(x) = x + 5, and f(x) = k(x) • m(x) · n(x). a. Determine the degree of the function f(x).​

Answer 1

`Degree = 3`

Explanation:

Given

`k(x) = x + 1`

`m(x) = x - 4`

`n(x) = x + 5`

`f(x) = k(x) * m(x) * n(x)`

Required

The degree of f(x)

First, calculate f(x)

`f(x) = k(x) * m(x) * n(x)`

`f(x) = (x +1) * (x - 4) * (x + 5)`

Expand

`f(x) = (x +1) * (x^2 - 4x + 5x - 20)`

`f(x) = (x +1) * (x^2 + x - 20)`

Further Expand

`f(x) = x^3 + x^2 - 20x +x^2 + x - 20`

Collect like terms

`f(x) = x^3 + x^2 +x^2 - 20x + x - 20`

`f(x) = x^3 + 2x^2 - 19x- 20`

The degree of f(x) is the highest power of x.

Hence:

`Degree = 3`