2017 · Q18
The product of the polynomials (x+2),(x-2),(x³-2x²+4x-8) and (x³+2x²+4x+8) is
Elementary MathematicsAlgebra
- Ax⁸-256
- B(x⁴-16)²
- C(x⁴+16)²
- D(x²-4)⁴
Explanation
Factor the cubics: x³−2x²+4x−8 = (x−2)(x²+4) and x³+2x²+4x+8 = (x+2)(x²+4). With (x+2)(x−2) = x²−4, the full product is (x²−4)(x−2)(x²+4)(x+2)(x²+4) = (x²−4)²(x²+4)² = [(x²−4)(x²+4)]² = (x⁴−16)². Hence option (B) (x⁴−16)².