0000:00:00:00:00Start31Number 31ExplanationIf the polynomial f(x)f(x)f(x) is divisible by (x−1)(x - 1)(x−1), then the remainder when f(x)f(x)f(x) is divided by (x−1)(x+1)(x - 1)(x + 1)(x−1)(x+1) is....−f(−1)2(1+x)\frac{-f(-1)}{2}(1 + x)2−f(−1)(1+x)−f(−1)2(1−x)\frac{-f(-1)}{2}(1 - x)2−f(−1)(1−x)f(−1)2(1+x)\frac{f(-1)}{2}(1 + x)2f(−1)(1+x)f(−1)2(1−x)\frac{f(-1)}{2}(1 - x)2f(−1)(1−x)f(−1)2(x−1)\frac{f(-1)}{2}(x - 1)2f(−1)(x−1)
31Number 31ExplanationIf the polynomial f(x)f(x)f(x) is divisible by (x−1)(x - 1)(x−1), then the remainder when f(x)f(x)f(x) is divided by (x−1)(x+1)(x - 1)(x + 1)(x−1)(x+1) is....−f(−1)2(1+x)\frac{-f(-1)}{2}(1 + x)2−f(−1)(1+x)−f(−1)2(1−x)\frac{-f(-1)}{2}(1 - x)2−f(−1)(1−x)f(−1)2(1+x)\frac{f(-1)}{2}(1 + x)2f(−1)(1+x)f(−1)2(1−x)\frac{f(-1)}{2}(1 - x)2f(−1)(1−x)f(−1)2(x−1)\frac{f(-1)}{2}(x - 1)2f(−1)(x−1)
