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Choose all of the following expressions which are even for all integer values of n.

2n + 10
n+2
4n - 6
3n + 12
2n + 5

1 Answer

6 votes

Answer:

2n + 10 and 4n - 6

Explanation:

To determine whether an expression is even for all integer values of n, we need to check if the expression is divisible by 2 for all integers.

Let's analyze each expression:

1. 2n + 10: This expression can be simplified to 2(n + 5). Since 2 is a factor of 2n for all integers n, and adding 5 does not affect the evenness, this expression is even for all integer values of n.

2. n + 2: This expression represents a linear function with a coefficient of 1. Adding a constant (2) to a linear function does not affect its evenness. Therefore, this expression is not even for all integer values of n.

3. 4n - 6: This expression can be simplified to 2(2n - 3). Since 2 is a factor of 2n for all integers n, and subtracting 3 does not affect the evenness, this expression is even for all integer values of n.

4. 3n + 12: This expression can be simplified to 3(n + 4). Since 3 is not a factor of n for all integers n, this expression is not even for all integer values of n.

5. 2n + 5: This expression represents a linear function with a coefficient of 2. Multiplying a linear function by a non-even number does not preserve its evenness. Therefore, this expression is not even for all integer values of n.

Expressions that are even for all integer values of n: 2n + 10 and 4n - 6.

User Safran Ali
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