2X^2-6y^2+3z^2-xy+7yz+7xz因式分解
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2X^2-6y^2+3z^2-xy+7yz+7xz因式分解2X^2-6y^2+3z^2-xy+7yz+7xz因式分解2X^2-6y^2+3z^2-xy+7yz+7xz因式分解对于复杂的多项式分解,待定
2X^2-6y^2+3z^2-xy+7yz+7xz因式分解
2X^2-6y^2+3z^2-xy+7yz+7xz因式分解
2X^2-6y^2+3z^2-xy+7yz+7xz因式分解
对于复杂的多项式分解,待定系数法很好用.
令2X^2-6y^2+3z^2-xy+7yz+7xz=(x+ay+bz)(2x+cy+dz)
原式=2x^2+(2a+c)xy+(2b+d)xz+acy^2+(ad+bc)yz+bdz^2
对比,得
2a+c=-1
2b+d=7
ac=-6
ad+bc=7
bd=3
解得
a=-2 b=3 c=3 d=1
2X^2-6y^2+3z^2-xy+7yz+7xz=(x-2y+3z)(2x+3y+z)
也可以直接用拆项的方法做,不过要麻烦一点.
2X^2-6y^2+3z^2-xy+7yz+7xz
=2x^2-xy-6y^2+3z^2+7yz+7xz
=(x-2y)(2x+3y)+6xz+9yz+xz-2yz+3z^2
=(x-2y)(2x+3y)+3z(2x+3y)+z(x-2y)+3z^2
=(x-2y+3z)(2x+3y+z)
2X^2-6y^2+3z^2-xy+7yz+7xz
=2x^2-xy-6y^2+3z^2+7yz+7xz
=(x-2y)(2x+3y)+6xz+9yz+xz-2yz+3z^2
=(x-2y)(2x+3y)+3z(2x+3y)+z(x-2y)+3z^2
=(x-2y+3z)(2x+3y+z)
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