閱讀下列材料,然后解答問(wèn)題:
問(wèn)題:分解因式:x
3-5x
2+4
解答:對(duì)于任意一元多項(xiàng)式f(x),其奇次項(xiàng)系數(shù)之和為m,偶次項(xiàng)系數(shù)之和為n,若m=n,則f(-1)=0,若m=-n,則f(1)=0.在x
3-5x
2+4中,因?yàn)閙=5,n=-5,所以把x=1代入多項(xiàng)式x
3-5x
2+4,得其值為0,由此確定多項(xiàng)式x
3-5x
2+4中有因式(x-1),于是可設(shè)x
3-5x
2+4=(x-1)(x
2+mx+n),分別求出m,n的值,再代入x
3-5x
2+4=(x-1)(x
2+mx+n),就容易分解多項(xiàng)式x
3-5x
2+4,這種分解因式的方法叫做“試根法”.
(1)上述式子中m=
-4
-4
,n=
-4
-4
;
(2)對(duì)于一元多項(xiàng)式x
3-x
2-17x-15,必定有f(
-1
-1
)=0;
(3)請(qǐng)你用“試根法”分解因式:x
3-x
2-17x-15.