The polynomial can be factored as (x + 2)(x + 2), indicating it has one real root with multiplicity 2.

Using the property of exponents, we have 2^(x+1 - (x-1)) = 2^(x+1-x+1) = 2^2.

Since 8 can be expressed as 2^3, we have 2^(x+3) = 2^3, thus x + 3 = 3, leading to x = 0.

Since 16 can be expressed as 4^2, we have 4^(x+1) = 4^2, leading to x + 1 = 2, thus x = 1.

Since 0.01 is 10^-2, log_10(0.01) = -2.

Using the property of logarithms that states log_a(b) - log_a(c) = log_a(b/c), we find log_2(8) - log_2(4) = log_2(8/4) = log_2(2).

Since 81 is 3^4, log_3(81) equals 4.

Logarithm of zero is undefined, hence log_5(0) is the correct answer.

The last identity is incorrect; it should be log_a(b) + log_a(c) = log_a(bc).

The Power Rule states that log_a(b^c) = c * log_a(b).

15 is the smallest common multiple of 3 and 5, and 30 is also a common multiple. However, 15 is the first one listed.

12 is the smallest common multiple of 4 and 6, and 24 is also a common multiple, but 12 is the smallest.

12 is a factor of 144 because 144 ÷ 12 = 12, which is an integer.

12 is a factor of 48, as 48 divided by 12 equals 4, which is an integer.

12 is a factor of 60 as 60 divided by 12 equals 5 with no remainder.

12 is the smallest number that is a multiple of both 4 and 6.

The LCM of 8 and 12 is 24, which is a multiple of both.

121 is divisible by 11, as 121 = 11 x 11.

A number is divisible by 15 if it is divisible by both 3 and 5. 30 meets both criteria.

28 is divisible by 7 (28 ÷ 7 = 4). The other numbers are not.

A number is divisible by 8 if the last three digits form a number that is divisible by 8. 64 is divisible by 8.

A number is divisible by both 2 and 5 if it ends in 0. 20 ends in 0, thus it is divisible by both.

7 is not a factor of 60, as 60 cannot be divided evenly by 7.

50 is not a multiple of 11, while the others are.

35 is not a multiple of 6, while 18, 24, and 30 are all multiples of 6.

To check divisibility by 11, subtract the last digit from the rest of the number. For 154, 15 - 4 = 11, which is divisible by 11. The others are divisible.

55 is not divisible by 12, as it does not meet the criteria of being divisible by both 3 and 4.

A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 22 (2 + 2 = 4) is not divisible by 3.

40 is not divisible by 7, while 21, 28, and 35 are all multiples of 7.

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. 90 is not divisible by 8.