Question

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

Answer 1

Answer:

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

Step-by-step 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