①(x+4)(x+9)
=x^2+13x+36
=x²+mx+36
m=13
②(x-2)(x-18)
=x^2-20x+36
=x²+mx+36
m=-20
③(x+3)(x+p)=x²+mx+36
=x^2+(3+p)x+3p
=x²+mx+36
3p=36
p=12
3+p=m
3+12=m
m=15
④(x-6)(x-p)=x²+mx+36
=x^2-(6+p)x+6p
=x²+mx+36
6p=36
p=6
-(6+p)=m
-(6+6)=m
m=-12
⑤(x+p)(x+q)=x²+mx+36,p,q為整數(shù)
(x+p)(x+q)
=x2+px+qx+pq
(p+q)x+pq=mx+36
∴pq=36,p+q=m
則⑴p=1,q=36,m=37 ⑵p=2,q=18,m=20 ⑶p=3,q=12,m=15
⑷p=4,q=9,m=13 ⑸p=6,q=6,m=12
上述5種情況變負(fù)為：-37,-20,-15,-13,-12
共10種情況．