因式分解(十字相乘法)07730教学提纲.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,因式分解,十字相乘法,1,.(x+2)(x+1)=,x,2,+3x+2,3,.(x-2)(x+1)=,x,2,-x-2,4,.(x-2)(x-1)=,x,2,-3x+2,2,.(x+2)(x-1)=,x,2,+x-2,5,.(x+2)(x+3)=,x,2,+5x+6,6,.(x+2)(x-3)=,x,2,-x-6,7,.(x-2)(x+3)=,x,2,+x-6,8,.(x-2)(x-3)=,x,2,-5x+6,(x+,a,)(x+,b,),=x,2,+(,a+b,)x+,ab,计算：,(x+2)(x+1),x,2,+3x+2,(x-2)(x+1),x,2,-x-2,(x-2)(x-1),x,2,-3x+2,(x+2)(x-1),x,2,+x-2,(x+2)(x+3),x,2,+5x+6,(x+2)(x-3),x,2,-x-6,(x-2)(x+3),x,2,+x-6,(x-2)(x-3),x,2,-5x+6,(x+a)(x+b),=,x,2,+(a+b)x+ab,=,=,=,=,=,=,=,=,1.,2.,3.,4.,5.,6.,7.,8.,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,.,1.x,2,+8x+12=,2.x,2,-11x-12=,练一练,3.x,2,-7x+12=,4.x,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，它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,5.x,2,+13x+12=,(x+1)(x+12),6.x,2,-x-12=,(x-4)(x+3),将下列各式因式分解,:,x,2,+,p,x+,q,=,x,2,+(,a,+,b,)x+,ab,=,x,x,a,b,a,x,+,b,x,=,(,a,+,b,)x,(x+,a,)(x+,b,),课堂小结,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：,1.,掌握方法：拆分常数项，验证一次项,.,2.,符号规律：,当,q0,时，,a,、,b,同号，且,a,、,b,的符号与,p,的符号相同；,当,q0,时，,a,、,b,异号，且绝对值较大的因数与,p,的符号相同,.,3.,书写格式：竖分横积,用十字相乘法进行因式分解：,(x+2)(x-3),1.x,2,-x-6=,(x-3)(x+5),2.x,2,+2x-15=,(x+2)(x-5),3.x,2,-3x-10=,(x-5)(x-4),4.x,2,-9x+20=,(x-7)(x+4),5.x,2,-3x-28=,(x+2)(x-4),6.x,2,-2x-8=,(x-1)(x-3),7.x,2,-4x+3=,(x+3)(x+4),(x+2)(x+3),(x-3)(x+7),8.x,2,+7x+12=,9.x,2,+5x+6=,10.x,2,+4x-21=,(y+12)(y-3),11.y,2,+9y-36=,(y-9)(y+14),(y+4)(y-15),(y-7)(y+16),(y-8)(y-17),(y+16)(y+3),(y+19)(y-7),(y+11)(y-10),(y-13)(y-3),(y+14)(y+4),13.y,2,-11y-60=,12.y,2,+5y-126=,14.y,2,+9y-112=,15.y,2,-25y+136=,16.y,2,+19y+48=,17.y,2,+12y-133=,18.y,2,+y-110=,19.y,2,-16y+39=,20.y,2,+18y+56=,先填空，再分解（尽可能多的）,2,(),=()(),拓展练习,