几道分解因式题分解因式(x^2-x-3)(x^2-x-5)-3=若2x^3-x^2+mx+n含有因式(x+2)(x-4),则m=_ n=_(x+1)(x+3)(x+5)(x+7)+15=整数a,b满足6ab=9a-10b+303,则a+b=已知多项式x^3+ax^2+bx+c含有因式(x+1)和(x-1),且被(x-2)除余3,则a=

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几道分解因式题分解因式(x^2-x-3)(x^2-x-5)-3=若2x^3-x^2+mx+n含有因式(x+2)(x-4),则m=_n=_(x+1)(x+3)(x+5)(x+7)+15=整数a,b满足6

几道分解因式题分解因式(x^2-x-3)(x^2-x-5)-3=若2x^3-x^2+mx+n含有因式(x+2)(x-4),则m=_ n=_(x+1)(x+3)(x+5)(x+7)+15=整数a,b满足6ab=9a-10b+303,则a+b=已知多项式x^3+ax^2+bx+c含有因式(x+1)和(x-1),且被(x-2)除余3,则a=
几道分解因式题
分解因式(x^2-x-3)(x^2-x-5)-3=
若2x^3-x^2+mx+n含有因式(x+2)(x-4),则m=_ n=_
(x+1)(x+3)(x+5)(x+7)+15=
整数a,b满足6ab=9a-10b+303,则a+b=
已知多项式x^3+ax^2+bx+c含有因式(x+1)和(x-1),且被(x-2)除余3,则a=_,b= c=

几道分解因式题分解因式(x^2-x-3)(x^2-x-5)-3=若2x^3-x^2+mx+n含有因式(x+2)(x-4),则m=_ n=_(x+1)(x+3)(x+5)(x+7)+15=整数a,b满足6ab=9a-10b+303,则a+b=已知多项式x^3+ax^2+bx+c含有因式(x+1)和(x-1),且被(x-2)除余3,则a=
1.
分解因式(x^2-x-3)(x^2-x-5)-3
设x^2-x=y
则(x^2-x-3)(x^2-x-5)-3
=(y-3)(y-5)-3
=y^2-8y+15-3
=y^2-8y+12
=(y-2)(y-6)
=(x^2-x-2)(x^2-x-6)
=(x+1)(x-2)(x+2)(x-3)
2.
设2x^3-x^2+mx+n=(x+2)(x-4)(2x+a)
而(x+2)(x-4)(2x+a)
=(x^2-2x-8)(2x+a)
=2x^3-4x^2-16x+ax^2-2ax-8a
=2x^3+(a-4)x^2-(2a+16)x-8a
所以令a-4=-1,m=-(2a+16),n=-8a
解得a=3,m=-22,n=-24
3.
(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(y+7)(y+15)+15
=y^2+22y+105+15
=y^2+22y+120
=(y+10)(y+12)
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
=(x+4-√6)(x+4+√6)(x+2)(x+6)
4.
整数a,b满足6ab=9a-10b+303,则a+b= ?
6ab=9a-10b+303
6ab+10b=9a+303
2b(3a+5)=9a+15+303-15
2b(3a+5)=3(3a+5)+288
2b(3a+5)-3(3a+5)=288
(2b-3)(3a+5)=288
因为a,b为整数,
所以2b-3为奇数
所以(2b-3)(3a+5)=288=1*288=(-1)*(-288)=3*96=(-3)*(-96)=9*32=(-9)(-32)
所以
当2b-3=1,3a+5=288得b=2,a=283/3不合题意,舍去
当2b-3=-1,3a+5=-288得b=1,a=-293/3不合题意,舍去
当2b-3=3,3a+5=96得b=3,a=91/3不合题意,舍去
当2b-3=-3,3a+5=-96得b=0,a=101/3不合题意,舍去
当2b-3=9,3a+5=32得b=6,a=9
当2b-3=-9,3a+5=-32得b=-3,a=-37/3不合题意,舍去
所以a=9,b=6,a+b=15
5.
设x^3+ax^2+bx+c
=(x+1)(x-1)(x+m)
=(x^2-1)(x+m)
=x^3+mx^2-x-m
则a=m,b=-1,c=-m
又设x^3+mx^2-x-m
=(x-2)(x^2+nx+p)+3
=x^3+(n-2)x^2+(p-2n)x+(3-2p)
则m=n-2,-1=p-2n,-m=3-2p
解得n=1,p=1,m=-1
所以a=m=-1,b=-1,c=-m=1
即a=-1,b=-1,c=1

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