Question

Determine whether g(x) is a factor of f(x) or not:

f(x) = x³ − x² − x − 2; g(x) = x − 2

Answer 1

Step 1: Convert g(x) to (x − a) form

x − 2 = 0

x = 2

Step 2: Evaluate the function:

We evaluate f(x) at x = 2

f(2) = 2³ − 2² − 2 − 2

= 8 − 4 − 2 − 2

= 0

Since f(2) = 0, g(x) is a factor of f(x).