Question

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.

Answer 1

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

Explanation:

Given

`x^2 + 2xn + n^2` --- the right expression

`n > 0`

Required

Possible values of n

`x^2 + 2xn + n^2`

Expand

`x^2 + 2xn + n^2 = x^2 + xn+xn + n^2`

Factorize

`x^2 + 2xn + n^2 = x(x + n)+n(x + n)`

Factor out
`x + n`

`x^2 + 2xn + n^2 = (x + n)(x + n)`

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

`x^2 + 2xn + n^2 = (x + n)^2`

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

Hence: (a) is correct