Mathematics Olympics of Grade Three

1.f (x) = what is the remainder of cube-3 (the square of x) +4x+5 divided by x-2?

2. Polynomial 2 (the fourth power of X)-3 (the third power of X)+A (the square of X) +a(x+B is divisible by (x+2)) (x- 1), and find the ratio of A to B.

3. Given a+b+c+d=0, it is proved that the cube of a+b+c+d =3(abc+bcd+cda+dab).

4. It is known that the square of 1 square +2 square +3 square+...+...+n =n/6(n+ 1)(2n+ 1). Find the value of 2 square +4 square+... +50 square.

Thank you, kind people, for helping me. Or I'll be miserable tomorrow.

An integer coefficient quartic polynomial f(x) has f(a)=f(b)=f(c)=f(d)= 1 for four different integers a, b, c and d, and it is proved that for any integer m, f(m)=- 1.

2. In view of this. X-x is 1=2. Find the value of cubic X-cubic x 1+ 1-2x.

3. Given a÷b=c÷d, find the seventh power of (A +b) ÷(c +d) -(a+b) ÷(c+d).

4. Let x ÷ (the square of x-MX+1) = 1, then what is the value of the cubic x ÷ (the sixth power of x-m * 3x * 3+1)?

5. If abc= 1, what is the value of A \ (AB+A+1)+B \ (BC+B+1)+C \ (AC+C+1)?

6. If a÷b=c÷d=e÷f, try to find N ÷(b +d +f)-(A+C +e).

7. Turn the cube of the fraction (x squared +2)÷(x- 1) into the algebraic sum of several fractions without X..

8. Given X = (a-b) ÷ (a+b). Y = (b-c) ÷ (b+c),Z = (c-a) ÷ (c+a),find ( 1+x) (65438)。

9. It is known that the univariate quadratic equation χ aχ2+(2a- 1)χ+a-3=0, and a is a positive integer. When a is a value, this equation has at least one integer root.

1 1, project a, received bids from teams A and B in the tender, as follows:

(1) A construction team works alone, and the daily project cost is 1.5 million yuan, and * * * takes n days to complete.

(2) Construction team B works alone, and the project cost is 1. 1 000 yuan/day, and * * * takes (n+5) days to complete.

(3) If Team A and Team B work together for 4 days, the rest of the work will be completed by Team B alone, which will take N days to complete.

Now the construction period is just n days, which construction scheme is the most economical? How many ten thousand yuan do you need to prepare at least for the project?