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# if x is a positive intiger ,is x^3-3x^2+2x divisible by 4?

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SVP
Joined: 05 Jul 2006
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if x is a positive intiger ,is x^3-3x^2+2x divisible by 4? [#permalink]  16 Sep 2006, 08:13
if x is a positive intiger ,is x^3-3x^2+2x divisible by 4?

1) x=4y+4, y is an intiger
2) x = 2z+2 , z is an intiger
Senior Manager
Joined: 31 May 2006
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Location: Phoenix AZ
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D.

the equation is x(x-1)(x-2)

both statements are equally good to determine divisibility by 4.
SVP
Joined: 01 May 2006
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(D) as well

St1 :
x=4*y+4
<=> x = 4*k'

Thus, 4 is a factor of x and hence, we can factorize by 4 in the equation (4*k')^3-3(4*k')^2+2(4*k') : divisible by 4
SUFF

St2 :
x=2*z+2
<=> x = 2*k''

Thus, x^3-3x^2+2x becomes 4*2*(k'')^3-3*4*(k'')^2+4*(k''), and hence, we can factorize by 4 : divisible by 4
SUFF
Manager
Joined: 30 Jan 2006
Posts: 64
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I think it is A

For the Statement 1 everybody has provided with an answer

We have to determine x(x-1)(x-2)

For S2
x = 2z+2 , z is an integer
now if z=0

x=2 and the equation becomes 0 and if 0 is divisble by 4 then i can say the answer is D.

Can anybody explain is 0 divisble by an any other no.?
Manager
Joined: 30 Jan 2006
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yezz!!! what is the OA?
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