Several mathematical problems about factorization in grade two of junior high school 1. If a + B + C = 1, then the result of polynomial a ^ 3 + A ^ 2B + BC ^ 2-abc + C ^ 3 should be 2. Given that X and y are positive integers and XY + 2x + y = 4, then the value of X and Y is? 3. It is known that one factor of the polynomial x ^ 2-4xy + 4Y ^ 2 + 2x-4y-3 is x-2y-1, then the other is x-2y-1 4. Given that X and y are positive integers, and x ^ 2-y ^ 2 = 121, what are the values of X and y? 5. When k=___ The polynomial x ^ 3 + KX ^ 2 + X-1 can be divided into several groups to decompose factors 6. If the polynomial a ^ 2-5A + M can be factorized by the collocation method, how many values of M? (in the range of rational numbers) To process. Everyone help!

Several mathematical problems about factorization in grade two of junior high school 1. If a + B + C = 1, then the result of polynomial a ^ 3 + A ^ 2B + BC ^ 2-abc + C ^ 3 should be 2. Given that X and y are positive integers and XY + 2x + y = 4, then the value of X and Y is? 3. It is known that one factor of the polynomial x ^ 2-4xy + 4Y ^ 2 + 2x-4y-3 is x-2y-1, then the other is x-2y-1 4. Given that X and y are positive integers, and x ^ 2-y ^ 2 = 121, what are the values of X and y? 5. When k=___ The polynomial x ^ 3 + KX ^ 2 + X-1 can be divided into several groups to decompose factors 6. If the polynomial a ^ 2-5A + M can be factorized by the collocation method, how many values of M? (in the range of rational numbers) To process. Everyone help!

1. B = 1-a-c, the original formula is a ^ 3 + A ^ 2-A ^ 3-A ^ 2C + C ^ 2-ac ^ 2-C ^ 3-ac + A ^ 2C + AC ^ 2 + C ^ 3,
That is a ^ 2 + C ^ 2-ac
2. X (y + 2) + (y + 2) = 6, that is, (x + 1) (y + 2) = 6 = (1 + 1) (1 + 2)
Since X and y are positive integers, let x = 1 + A and y = 1 + B. If a and B are both non negative integers, then (2 + a) (3 + b) = 6, that is ab + 2B + 3A = 0
Since a and B are both > = 0, it can only be a = b = 0, then x = y = 1
3. x-2y+3
4. (x+y)(x-y)=11*11=1*121
When 11 * 11 is chosen on the right, that is, x + y = X-Y = 11, then y = 0 is not suitable
So take 1 * 121 on the right, then x + y = 121, X-Y = 1, then x = 61, y = 60
5. X ^ 2 (x + k) + (x-1), when k = - 1, it can be decomposed;
6. That is (a-5 / 2) ^ 2 - (25 / 4-m), when using the formula method of rational number, (25 / 4-m) must be the square of a rational number x, then M = 25 / 4-x ^ 2, so m can still take infinite values between 0 and 25 / 4. If you limit integers and the like, there will be limited values