Correct Answer - Option 3 : Both (2x + 1) and (2x - 1)
Given:
The polynomial is 4x3 + 12x2 - x - 3
Calculation:
We can check whether (2x + 1) and (2x - 1) are factor of the polynomial or not
Check for (2x + 1)
2x + 1 = 0
⇒ x = -1/2
Putting this value in the polynomial we'll get
4(-1/2)3 + 12(-1/2)2 - (-1/2) - 3
⇒ -1/2 + 3 + 1/2 - 3 = 0
(2x + 1) is a factor of the polynomial
Check for (2x - 1)
2x - 1 = 0
⇒ x = 1/2
Putting this value in the polynomial we'll get
4(1/2)3 + 12(1/2)2 - (1/2) - 3
⇒ 1/2 + 3 - 1/2 - 3 = 0
(2x - 1) is a factor of the polynomial
∴ 4x3 + 12x2 - x - 3 is divisible by both (2x + 1) and (2x - 1)
