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