一、填空題
(1)x2+2x-15=(x-3)(_____)
(2)6xy-x2-5y2=-(x-y)(_____).
(3)________=(x+2)(x-3).
(4)分解因式x2+6x-7=__________.
(5)若多項式x2+bx+c可分解為(x+3)(x-4),則b=_____,c=_____.
(6)若x2+7x=18成立,則x值為_____.
(7)若x2-3xy-4y2=0,且x+y≠0,則x=_____.
(8)(x-y)2+15(x-y)+14=(_____+1)(x-y+_____).
(9)多項式 x2+3x+2,x2-2x-8,x2+x-2的公因式為_____.
(10)已知a,b為整數(shù),且m2-5m-6=(m+a)(m+b),則a=_____,b=_____.
三、因式分解
(1) x(x+y+z)+yz (2) x2m+xm+
(3) a2b2-a2-b2-4ab+1
(4) a2(x-y)2-2a(x-y)3+(x-y)4
(5) x4-6x2+5
(6) x4-7x2+1 (7) 3a8-48b8
(8) x2+4y2+9z2-4xy-6xz+12yz
1.已知a2+9b2-2a+6b+2=0,求a,b的值.
2.求證：不論x取什么有理數(shù),多項式-2x4+12x3-18x2的值都不會是正數(shù).
3.已知n為正整數(shù),試證明(n+5)2-(n-1)2的值一定被12整除.
4.已知x+y=4,xy=3,求(1) 3x2+3y2; (2) (x-y)2.
5.設(shè)a>0,b>0,c>0且a、b、c中任意兩數(shù)之和大于第三個數(shù),求證：a2-b2-c2-2bc