When one term (the "dividend") is divided by another term (the "divisor"), the result is a "quotient" and a "remainder".

When the remainder is zero, the dividend is divisible by both the divisor and the quotient.

When the remainder is NOT zero, the dividend is NOT divisible by the divisor or by the quotient.

6 is the dividend.

3 is the divisor.

2 is the quotient.

0 is the remainder.

Since the remainder is zero, 6 is divisible by both both 2 and 3.

7 is the dividend.

3 is the divisor.

2 is the quotient.

1 is the remainder.

Since the remainder is not zero, 7 is not divisible by 2 or by 3.

6x - 15 is the dividend.

3 is the divisor.

2x - 5 is the quotient.

0 is the remainder.

Since the remainder is zero, 6x - 15 is divisible by both 3 and 2x - 5.

6x - 15 is the dividend.

3x is the divisor.

2 is the quotient.

-15 is the remainder.

Since the remainder is not zero, 6x - 15 is not divisible by 3x or by 2.

Please note that there are divisibility rules for divisors that are small numbers that can make checking for divisibility easier.