1. Given a polynomial f(x) whose degree is no less than 3. The remainders of f(x) being divided by (x − a)(x − b), (x − b)(x − c), (x − a)(x − c) are −x − 5, 4x, 3x + 3 respectively. Find the remainder of f(x) being divided by (x − a)(x − b)(x − c).

1. There was a class of 41 people divided into three groups A, B, and C, and the average score of subject natural’s test was 89.7 points; the average score of group A was 89.8 points; the average score of A, B combination was 88.5 points; the average score of A and C combination was 91 points, and how many people were in each of groups A, B and C?

1. Given a polynomial f(x) whose degree is no less than 3. The remainders of f(x) being divided by (x − a)(x − b), (x − b)(x − c), (x − a)(x − c) are −x − 5, 4x, 3x + 3 respectively. Find the remainder of f(x) being divided by (x − a)(x − b)(x − c).

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