Question

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

f(x) = 4x² + 7x − 3; g(x) = 2x + 3

Answer 1

Step 1: Convert g(x) to (x – a) form

2x + 3 = 0

x = `−3/2`

Step 2: Evaluate the function:

We evaluate f(x) at x = `−3/2`

`f(−3/2) = 4(−3/2)^2 + 7(−3/2) - 3`

= `4(9/4) -21/2 -3`

= 9 − 10.5 − 3

= 9 − 13.5

= −4.5

Since `f (-3/2)` ≠ 0

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