What about n + 3n + 2? WILL it also bee even

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04-11-2022
Mathematics

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What about n + 3n + 2? WILL it also bee even

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LilahY654208 LilahY654208 · Answer 1 · 2022-11-04T00:02:13-04:00

ANSWER

n² + 3n + 2 is always even

EXPLANATION

The expression n² + 3n + 2 can be factorized. The zeros are 1 and 2,

[tex]n^2+3n+2=(n+2)(n+1)[/tex]

Let's say that n is odd. In that case, the result of the first factor (n + 2) is an odd number, while the result of the second factor, (n + 1) is an even number. The product of an even number and an odd number is even, so we proved that if n is odd, then the expression is even.

Let's say now that n is even. The result of adding 2 to an even number, like in the first factor, is another even number. The result of the second factor, on the other hand, is an odd number. Like we stated before when n was odd, the result of multiplying any number by an even number is an even number.

Hence, n² + 3n + 2 is always even.

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