數學題(20分)

1a)

i) 2z^3-12z^2+18z

=2z(z^2)-2z(6z)+2z(9)

=2z(z^2-6z+9)

=2z[z^2-2(z)(3)+3^2]

=2z(z-3)^2



ii) 2(x+1)^3-12(x+1)^2+18(x+1)

In (a)(i), let z=x+1, we have

2(x+1)^3-12(x+1)^2+18(x+1)

= 2z^3-12z^2+18z

=2z(z-3)^2 (Result of (a)(i))

=2(x+1)(x+1-3)^2 (z=x+1)

=2(x+1)(x-2)^2



1b)

Height of the cuboid = [2(x+1)^3-12(x+1)^2+18(x+1)] / (x-2)^2

= 2(x+1)(x-2)^2 / (x-2)^2 (Result of (a)(ii))

= 2(x+1)

2006-12-30 15:05:59 補充：
1c)The area of the square = [2(x＋1)]^2= 4(x＋1)^2=4(x^2＋2x＋1)=4x^2＋8x＋4Because it also equals to Ax^2＋Bx＋C, we have4x^2＋8x＋4 = Ax^2＋Bx＋CBy comparing the like terms in LHS and RHS, we haveA=4, B=8, C=4

a)(i) 2(z 3次方) - 12(z 2次方) + 18z
= 2z[(z 2次方)-6z+9]
= 2z[(z-3)2次方]

a)(ii) 2[(x+1) 3次方] - 12[(x+1) 2次方] +18(x+1)
= 2(x+1)[(x+1-3)2次方]
= 2(x+1)[(x-2)2次方]

b) ｛2[(x+1) 3次方] - 12[(x+1) 2次方] +18(x+1)｝/ [(x-2)2次方]
= 2(x+1)[(x-2)2次方] / [(x-2)2次方]
= 2(x+1)

c) A=1
B=-4
C=4

1a) (i) Factorize 2(z 3次方) - 12(z 2次方) + 18z
(ii) using the result of (a)(i), factorize 2[(x+1) 3次方] - 12[(x+1) 2次方] +18(x+1)
(b) The base of a cuboid is a square with sides of (x-2)cm each. Given that the volume of the cuboid is factorize ｛2[(x+1) 3次方] - 12[(x+1) 2次方] +18(x+1)｝cm 3次方,using the result of (a), express the height of the cuboid in terms of =154