AbdurRakib wrote:
If k is a positive integer, what is the remainder when (k + 2)(k³ – k) is divided by 6 ?
A. 0
B. 1
C. 2
D. 3
E. 4
Alternatively, we can
plug in any positive integer for k and see what happens.
Try
k = 1We get: (k + 2)(k³ – k) = (
1 + 2)(
1³ –
1)
= (3)(0)
= 0
When we divide 0 by 6 we get 0 with remainder
0Answer: A
Just for "fun," let's test another k-value
Try
k = 2We get: (k + 2)(k³ – k) = (
2 + 2)(
2³ –
2)
= (4)(6)
= 24
When we divide 24 by 6 we get 4 with remainder
0Answer: still A
Try
k = 3We get: (k + 2)(k³ – k) = (
3 + 2)(
3³ –
3)
= (5)(24)
= 120
When we divide 120 by 6 we get 20 with remainder
0Answer: still A
And so on...
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