文档介绍：因式分解十字相乘法 1 .(x+2)(x+1)= x x 2 2+3x+2 +3x+2 3 3.(x-2)(x+1)= .(x-2)(x+1)= x x 2 2-x-2 -x-2 4 4.(x-2)(x-1)= .(x-2)(x-1)= x x 2 2-3x+2 -3x+2 2 2.(x+2)(x-1)= .(x+2)(x-1)= x x 2 2+x-2 +x-2 5 5.(x+2)(x+3)= .(x+2)(x+3)= x x 2 2+5x+6 +5x+6 6 6.(x+2)(x-3)= .(x+2)(x-3)= x x 2 2-x-6 -x-6 7 7.(x-2)(x+3)= .(x-2)(x+3)= x x 2 2+x-6 +x-6 8 8.(x-2)(x-3)= .(x-2)(x-3)= x x 2 2-5x+6 -5x+6 ( (x+ x+a a)(x+ )(x+ b b) )=x =x 2 2+( +(a+b a+b )x+ )x+ ab ab 请直接口答计算结果: (x+2)(x+1) x x 2 2+3x+2 +3x+2 (x-2)(x+1) (x-2)(x+1) x x 2 2-x-2 -x-2 (x-2)(x-1) (x-2)(x-1) x x 2 2-3x+2 -3x+2 (x+2)(x-1) (x+2)(x-1) x x 2 2+x-2 +x-2 (x+2)(x+3) (x+2)(x+3) x x 2 2+5x+6 +5x+6 (x+2)(x-3) (x+2)(x-3) x x 2 2-x-6 -x-6 (x-2)(x+3) (x-2)(x+3) x x 2 2+x-6 +x-6 (x-2)(x-3) (x-2)(x-3) x x 2 2-5x+6 -5x+6 ( (x+a)(x+b x+a)(x+b ) )= =x x 2 2+(a+b)x+ab +(a+b)x+ab = = = == = = == == == == = . 分解因式分解因式: :x x 2 2 +4x+3= +4x+3= x x 2 2 -2x-3= -2x-3= ?利用十字交叉线来分解系数,把二次三项式分解因式的方法叫做十字相乘法. 2+8x+12= 2-11x-12= 2-7x+12= 2-4x-12= (x+2)(x+6) (x-6)(x+2) (x-3)(x-4) (x-12)(x+1) ?符号规律: 常数项是正数时,应分解为两个因数,他们的符号与一次项系数符号; 常数项是负数时,应分解为两个因数,其绝对值的因数与一次项系数的符号相同. 同号相同异号较大 2+13x+12= (x+1)(x+12) 2-x-12= (x-4)(x+3) 将下列各式因式分解:x x 2 2+ +p px+ x+q q = =x x 2 2+( +(a a+ +b b)x+ )x+ ab ab = =xx abax+bx= ( (a a+ +b b)x )x ( (x+ x+a a)(x+ )(x+ b b) ) 对二次三项式 x 2+px+q 进行因式分解,应重点掌握以下三个问题: :拆分常数项,验证一次项. : 当q>0 时, a、b同号,且 a、b的符号与 p的符