Classify each as true or false. if the statement is true, identify the theorem. if the statement is false, give a counter example to show it is false.

a) true.

if 3 can divide a without remainder, then a = 3×x.

doubling that number makes it 2×3×x. because of that still included factor 3, it is still divisible by 3 without remainder.

b) false.

example :

a=6, b=4, c=3

bc = 12

6 can divide 12 without remainder, but 6 cannot do that with 4 and not with 3.

or

a=7, b=35, c=10

bc=350

7 can divide 350 without remainder, and can do that also with 35, but not with 10.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i