笔算实在是不知道怎么算,就用MATLAB计算.我已经计算了当k=-10000到10000的每个值时能不能因式分解的情况了,发现只有4个k值能行,分别是k=-2或k=-1或k=0或k=1,因此怀疑k值只能有四种情况.但是你题目说k是正整数,所以只能是k=1.以下是当k=-100到100的情况(全部写进来装不下). 　　>>symsx;k=-100:100;Z=x.^4-x.^3+k.*x.^2-2.*k.*x-2;Z=factor(Z) 　　Z= 　　[x^4-x^3-100*x^2+200*x-2,x^4-x^3-99*x^2+198*x-2,x^4-x^3-98*x^2+196*x-2,x^4-x^3-97*x^2+194*x-2,x^4-x^3-96*x^2+192*x-2,x^4-x^3-95*x^2+190*x-2,x^4-x^3-94*x^2+188*x-2,x^4-x^3-93*x^2+186*x-2,x^4-x^3-92*x^2+184*x-2,x^4-x^3-91*x^2+182*x-2,x^4-x^3-90*x^2+180*x-2,x^4-x^3-89*x^2+178*x-2,x^4-x^3-88*x^2+176*x-2,x^4-x^3-87*x^2+174*x-2,x^4-x^3-86*x^2+172*x-2,x^4-x^3-85*x^2+170*x-2,x^4-x^3-84*x^2+168*x-2,x^4-x^3-83*x^2+166*x-2,x^4-x^3-82*x^2+164*x-2,x^4-x^3-81*x^2+162*x-2,x^4-x^3-80*x^2+160*x-2,x^4-x^3-79*x^2+158*x-2,x^4-x^3-78*x^2+156*x-2,x^4-x^3-77*x^2+154*x-2,x^4-x^3-76*x^2+152*x-2,x^4-x^3-75*x^2+150*x-2,x^4-x^3-74*x^2+148*x-2,x^4-x^3-73*x^2+146*x-2,x^4-x^3-72*x^2+144*x-2,x^4-x^3-71*x^2+142*x-2,x^4-x^3-70*x^2+140*x-2,x^4-x^3-69*x^2+138*x-2,x^4-x^3-68*x^2+136*x-2,x^4-x^3-67*x^2+134*x-2,x^4-x^3-66*x^2+132*x-2,x^4-x^3-65*x^2+130*x-2,x^4-x^3-64*x^2+128*x-2,x^4-x^3-63*x^2+126*x-2,x^4-x^3-62*x^2+124*x-2,x^4-x^3-61*x^2+122*x-2,x^4-x^3-60*x^2+120*x-2,x^4-x^3-59*x^2+118*x-2,x^4-x^3-58*x^2+116*x-2,x^4-x^3-57*x^2+114*x-2,x^4-x^3-56*x^2+112*x-2,x^4-x^3-55*x^2+110*x-2,x^4-x^3-54*x^2+108*x-2,x^4-x^3-53*x^2+106*x-2,x^4-x^3-52*x^2+104*x-2,x^4-x^3-51*x^2+102*x-2,x^4-x^3-50*x^2+100*x-2,x^4-x^3-49*x^2+98*x-2,x^4-x^3-48*x^2+96*x-2,x^4-x^3-47*x^2+94*x-2,x^4-x^3-46*x^2+92*x-2,x^4-x^3-45*x^2+90*x-2,x^4-x^3-44*x^2+88*x-2,x^4-x^3-43*x^2+86*x-2,x^4-x^3-42*x^2+84*x-2,x^4-x^3-41*x^2+82*x-2,x^4-x^3-40*x^2+80*x-2,x^4-x^3-39*x^2+78*x-2,x^4-x^3-38*x^2+76*x-2,x^4-x^3-37*x^2+74*x-2,x^4-x^3-36*x^2+72*x-2,x^4-x^3-35*x^2+70*x-2,x^4-x^3-34*x^2+68*x-2,x^4-x^3-33*x^2+66*x-2,x^4-x^3-32*x^2+64*x-2,x^4-x^3-31*x^2+62*x-2,x^4-x^3-30*x^2+60*x-2,x^4-x^3-29*x^2+58*x-2,x^4-x^3-28*x^2+56*x-2,x^4-x^3-27*x^2+54*x-2,x^4-x^3-26*x^2+52*x-2,x^4-x^3-25*x^2+50*x-2,x^4-x^3-24*x^2+48*x-2,x^4-x^3-23*x^2+46*x-2,x^4-x^3-22*x^2+44*x-2,x^4-x^3-21*x^2+42*x-2,x^4-x^3-20*x^2+40*x-2,x^4-x^3-19*x^2+38*x-2,x^4-x^3-18*x^2+36*x-2,x^4-x^3-17*x^2+34*x-2,x^4-x^3-16*x^2+32*x-2,x^4-x^3-15*x^2+30*x-2,x^4-x^3-14*x^2+28*x-2,x^4-x^3-13*x^2+26*x-2,x^4-x^3-12*x^2+24*x-2,x^4-x^3-11*x^2+22*x-2,x^4-x^3-10*x^2+20*x-2,x^4-x^3-9*x^2+18*x-2,x^4-x^3-8*x^2+16*x-2,x^4-x^3-7*x^2+14*x-2,x^4-x^3-6*x^2+12*x-2,x^4-x^3-5*x^2+10*x-2,x^4-x^3-4*x^2+8*x-2,x^4-x^3-3*x^2+6*x-2,(x-1)*(x^3-2*x+2),(x^2-x+1)*(x^2-2),(x+1)*(x^3-2*x^2+2*x-2),(x^2-x-1)*(x^2+2),x^4-x^3+2*x^2-4*x-2,x^4-x^3+3*x^2-6*x-2,x^4-x^3+4*x^2-8*x-2,x^4-x^3+5*x^2-10*x-2,x^4-x^3+6*x^2-12*x-2,x^4-x^3+7*x^2-14*x-2,x^4-x^3+8*x^2-16*x-2,x^4-x^3+9*x^2-18*x-2,x^4-x^3+10*x^2-20*x-2,x^4-x^3+11*x^2-22*x-2,x^4-x^3+12*x^2-24*x-2,x^4-x^3+13*x^2-26*x-2,x^4-x^3+14*x^2-28*x-2,x^4-x^3+15*x^2-30*x-2,x^4-x^3+16*x^2-32*x-2,x^4-x^3+17*x^2-34*x-2,x^4-x^3+18*x^2-36*x-2,x^4-x^3+19*x^2-38*x-2,x^4-x^3+20*x^2-40*x-2,x^4-x^3+21*x^2-42*x-2,x^4-x^3+22*x^2-44*x-2,x^4-x^3+23*x^2-46*