Question

NO LINKS!!!

Use the factor theorem to show that x - c is a factor of f(x).

f(x) = x^4 - 16; c = -2

f(-2) = _____________

Answer 1

f(-2) = 0

Explanation:

Factor Theorem

If f(x) is a polynomial, and f(c) = 0, then (x – c) is a factor of f(x).

Given function:

`f(x) = x^4 - 16`

Substitute x = -2 into the given function:

`\begin{aligned}\implies f(-2)&=(-2)^4-16\\&=16-16\\&=0\end{aligned}`

As f(-2) = 0, this proves that (x + 2) is a factor of f(x).