Question

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

f(x) = 5x³ + x − 6; g(x) = x − 1

Answer 1

Step 1: Convert g(x) to (x − a) form

x − 1 = 0

x = 1

Step 2: Evaluate the function:

We evaluate f(x) at x = 1

f(1) = 5(1)³ + 1 − 6

= 5 + 1 − 6

= 0

Since f(1) = 0, g(x) is a factor of f(x).