2021 · Q75
4x³ + 12x² − x − 3 is divisible by
Elementary MathematicsAlgebra
- A(2x + 1) only
- B(2x − 1) only
- CBoth (2x + 1) and (2x − 1)
- DNeither (2x + 1) nor (2x − 1)
Explanation
f(−1/2) = 4(−1/8) + 12(1/4) + 1/2 − 3 = 0 and f(1/2) = 4(1/8) + 12(1/4) − 1/2 − 3 = 0. Since both ±1/2 are roots, the polynomial is divisible by both (2x+1) and (2x−1). Hence option C.