分解因式X^2代表X的平方X^3-3X^2+42X^4-11X^3+22X^2-19X+62X^3-X^2Z-4X^2Y+2XYZ+2XY^2-Y^2Z16M^2-16N^2+8M+1X^4+2X^3+3X^2+2X+1

Question

分解因式
X^2代表X的平方
X^3-3X^2+4
2X^4-11X^3+22X^2-19X+6
2X^3-X^2Z-4X^2Y+2XYZ+2XY^2-Y^2Z
16M^2-16N^2+8M+1
X^4+2X^3+3X^2+2X+1

Answer 1

X^3-3X^2+4
=X^3+X^2-4X^2+4
=X^2(X+1)-4(X+1)(X-1)
=(X+1)(X^2-4X+4)
=(X+1)(X-2)^2
2X^4 - 11X^3 + 22X^2 - 19X + 6
=(2X^4-2)-(11X^3-11)+22X^2-19X-3
=2(X^2+1)(X+1)(X-1)-11(X-1)(X^2+X+1)+(22X+3)(X-1)
=(X-1)(2X^3+2X^2+2X+2-11X^2-11X-11+22X+3)
=(X-1)(2X^3-9X^2+13X-6)
=(X-1)[(2X^3-2)-(9X^2-13X+4)]
=(X-1)[2(X-1)(X^2+X+1)-(9X-4)(X-1)]
=(X-1)^2(2X^2+2X+2-9X+4)
=(X-1)^2(2X^2-7X+6)
=(X-1)^2(X-2)(2X-3)
2X^3-X^2Z-4X^2Y+2XYZ+2XY^2-Y^2Z
=X^2(2X-Z)-2XY(2X-Z)+Y^2(2X-Z)
=(X^2-2XY+Y^2)(X-Z)
=(X-Y)^2(X-Z)
16M^2-16N^2+8M+1
=(4M+1)^2-(4N)^2
=(4M+4N+1)(4M-4N+1)
X^4+2X^3+3X^2+2X+1
=(X^4+2X^2+1)+(X^3+X)+(X^3+X^2+X)
=(X^2+1)^2+X(X^2+1)+X(X^2+X+1)
=(X^2+1)(X^2+1+X)+X(X^2+X+1)
=(X^2+1+X)(X^2+X+1)
=(X^2+X+1)^2