Question

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

f(x) = 6x³ − x + 3; g(x) = 2x + 1

Answer 1

Step 1: Convert g(x) to (x − a) form

2x + 1 = 0

2x = −1

x = `−1/2`

Step 2: Evaluate the function:

We evaluate f(x) at x = `−1/2`

`f(−1/2) = 6(−1/2)^3 − (−1/2) + 3`

= `6(−1/8) + 1/2 + 3`

= `−3/4 + 2/4 + 12/4`

= `11/4`

Since `f(−1/2)` ≠ 0

Therefore, g(x) is not a factor of f(x).