一、填空题
(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)若多项式x2+bx+c可分解为(x+3)(x-4),则b=_____,c=_____.
(6)若x2+7x=18成立,则x值为_____.
(7)若x2-3xy-4y2=0,且x+y≠0,则x=_____.
(8)(x-y)2+15(x-y)+14=(_____+1)(x-y+_____).
(9)多项式 x2+3x+2,x2-2x-8,x2+x-2的公因式为_____.
(10)已知a,b为整数,且m2-5m-6=(m+a)(m+b),则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.求证：不论x取什么有理数,多项式-2x4+12x3-18x2的值都不会是正数.
3.已知n为正整数,试证明(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.设a>0,b>0,c>0且a、b、c中任意两数之和大于第三个数,求证：a2-b2-c2-2bc