因式分解X(1+X)+X(1+X)^2+X+16A^4-5A^3-4A^24M^2+8MN+3N^2X^4+7X-185A^2B^2+23AB-105X^2+7X-63A^2-8A+42X^2+15X+7X^4-10X^2+93X^2+8X-32X^2-5X-3

Question

因式分解
X(1+X)+X(1+X)^2+X+1
6A^4-5A^3-4A^2
4M^2+8MN+3N^2
X^4+7X-18
5A^2 B^2+23AB-10
5X^2+7X-6
3A^2-8A+4
2X^2+15X+7
X^4-10X^2+9
3X^2+8X-3
2X^2-5X-3

Answer 1

⑴ X(1+X)+X(1+X)^2+(X+1) = (1+X)( X+X(1+X)+1 ) = (1+X)( X²+2X+1) = (1+X)³
⑵ 6A^4-5A^3-4A^2 = A²(6A²-5A-4) = A²(2A+1)(3A-4)
⑶ 4M^2+8MN+3N^2 = (2M+3N)(2M+N)
⑷ X^2+7X-18 = (X-2)(X+9) (题有误吧可能是 X^2不是X^4)
⑸ 5A^2 B^2+23AB-10 = (AB+5)(5AB-2)
⑹ 5X^2+7X-6 = (X+2)(5X-3)
⑺ 3A^2-8A+4 = (A-2)(3A-2)
⑻ 2X^2+15X+7 = (X+7)(2X+1)
⑼ X^4-10X^2+9 = (X²-1)(X²-9)
⑽ 3X^2+8X-3 = (3X-1)(X+3)
⑾ 2X^2-5X-3 = (X-3)(2X+1)