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Suppose you want to factor the expression x2 + 2xn+n?. Given that n>0, what are the factors? Explain.

Select the correct answer below and, if necessary, fill in the answer box to complete your choice.

O A. The value of n can be any positive integer resulting in the same factor

O B. The value of n can be any positive integer resulting in the distinct factors

(Use a comma to separate answers as needed.)

O C. The value of n can be any prime integer resulting in the same factor

O

D. The value of n can be any prime integer resulting in the distinct factors

(Use a comma to separate answers as needed.)

O E. The expression cannot be factored for the given values of n.

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MrRoyal

Answer:

A. The value of n can be any positive integer resulting in the same factor

Step-by-step explanation:

Given

[tex]x^2 + 2xn + n^2[/tex] --- the right expression

[tex]n > 0[/tex]

Required

Possible values of n

[tex]x^2 + 2xn + n^2[/tex]

Expand

[tex]x^2 + 2xn + n^2 = x^2 + xn+xn + n^2[/tex]

Factorize

[tex]x^2 + 2xn + n^2 = x(x + n)+n(x + n)[/tex]

Factor out [tex]x + n[/tex]

[tex]x^2 + 2xn + n^2 = (x + n)(x + n)[/tex]

From the expression above, we can see that the result has the same factor. This means that options (b), (d) and (e) are not possible

[tex]x^2 + 2xn + n^2 = (x + n)^2[/tex]

The above also shows that n can take any positive value.

Hence: (a) is correct

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