因式分解1條

9(a) 解：c^2 - 8c - 20
= c^2 + [2 + (-10)]c + [2 x (-10)]
= ( c - 10 ) ( c + 2 )

9(b) 解：y^2(y-3)^2 - 8y(y-3) - 20
= [y(y-3)]^2 - 8y(y-3) - 20
視 y( y - 3 ) 為 c ，則原式= c^2 - 8c - 20
= ( c - 10 ) ( c + 2 )
= [ y(y-3) - 10 ] [ y(y-3) + 2 ]
=( y^2 - 3y - 10 ) ( y^2 - 3y + 2 )
=( y - 5 ) ( y + 2 ) ( y - 1 ) ( y - 2 )

9(a) c^2-8c-20
=c^2+(2-10)c+(-10)(2)
=(c-10)(c+2)

9(b) y^2(y-3)^2-8y(y-3)-20
=[y(y-3)]^2+(2-10)y(y-3)+(-10)(2)
=[y(y-3)-10][y(y-3)+2]
=(y^2-3y-10)(y^2-3y+2)
=(y-5)(y+2)(y-2)(y-1)

9(a)因式分解c^2－8c－20
Sol
c^2－8c－20
=c^2+2c－10c－20
=c(c+2)－10(c+2)
=(c－10)(c+2)
9(b)以以上結果,因式分解y^2(y－3)^2－8y(y－3)－20
Sol
y^2(y－3)^2－8y(y－3)－20
=(y^2－3y)^2－8(y^2－3y)－20
=(y^2－3y－10)(y^2－3y+2)
=(y^2－5y+2y－10)(y^2－2y－y+2)
=[y(y－5)+2(y－5)][y(y－2)－(y－2)]
=(y+2)(y－5)(y－1)(y－2)