若x^2-10x+25-4y^2=(x+2y-5)(x+ay+b)則2a-b為?因式分解x^3-3x^2-4x+12=?因式分解12x^2+13x(x+1)-14(x+1)^2=?已知2014=2*19*53設x^2-15x-2014=(x+a)(x+b)且0>b則a-b之值為?

1 若x^2－10x+25－4y^2=(x+2y－5)(x+ay+b)則2a－b為?
Sol
(x+2y－5)(x+ay+b)
=x(x+ay+b)+2y(x+ay+b)－5(x+ay+b)
=(x^2+axy+bx)+(2xy+2ay^2+2by)+(－5x－5ay－5b)
=x^2+(a+2)xy+2ay^2+(b－5)x+(2b－5a)y－5b
a+2=0，2a=－4，b－5=－10，2b－5a=0，－5b=25
a=－2
b=－5
2a－b=－4+5=1
2 因式分解x^3－3x^2－4x+12=?
Sol
x^3－3x^2－4x+12
=(x^3－3x^2)+(－4x+12)
=x^2(x－3)－4(x－3)
=(x^2－4)(x－3)
=(x－2))(x+2)(x－3)
3 因式分解12x^2+13x(x+1)－14(x+1)^2=?
Sol
12x^2+13x(x+1)－14(x+1)^2
=12x^2+13x^2+13x－14x^2－28x－14
=11x^2－15x－14
=(11x+7)(x－2)
4 已知2014=2*19*53設x^2－15x-2014=(x+a)(x+b)且0>b則a－b之值為?
Sol
2014=2*19*53=38*53
53－38=15
x^2－15x－2014
=(x^2－53x)+(38x－2014)
=x(x－53)+38(x－53)
=(x+38)((x－53)
a=38－b=－53
a－b=38+53=91