MGMT Guide 1 DS question???

[gxj007]

Page 136 of Guide 1 gives the following DS example but I don't understand how statement 2 is sufficient???

If x is a positive integer, is x^3-3x^2+2x divisible by 4?

When factored this equation becomes 3 consecutive integers x(x-1)(x-2).

statement 2) x=2z+2, where z is an integer.

The answer explains that this statement is sufficient because x will always be even. But if z=0, then x=2 which is even but when you plug it into the equation you get 2(1)(0)=0. So is zero considered a multiple of 4???? I would think the product we have to be 4,8,12,etc.

thanks!

[Ian Stewart]

Page 136 of Guide 1 gives the following DS example but I don't understand how statement 2 is sufficient???

If x is a positive integer, is x^3-3x^2+2x divisible by 4?

When factored this equation becomes 3 consecutive integers x(x-1)(x-2).

statement 2) x=2z+2, where z is an integer.

The answer explains that this statement is sufficient because x will always be even. But if z=0, then x=2 which is even but when you plug it into the equation you get 2(1)(0)=0. So is zero considered a multiple of 4???? I would think the product we have to be 4,8,12,etc.

thanks!

Yes, zero is a multiple of 4, since we can get zero by multiplying 4 by an integer - namely by zero. For this reason, zero is a multiple of every positive integer (and is divisible by every positive integer).