How do you factor $x^(2n) + 10xn + 16$ ?

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Answer 1 · 2015-06-28T08:45:19

Assuming the expression is $x^(2n)+10x^n+16$

$x^(2n)+10x^n+16 = (x^n + 2)(x^n + 8)$

Whether this can be factored further depends on the value of $n$

$x^(2n)+10x^n+16 = (x^n)^2+10(x^n)+16$

is quadratic in $x^n$ and can be factored as:

$(x^n)^2+10(x^n)+16 = (x^n + 2)(x^n + 8)$

If you prefer, let $y = x^n$ .

Then

$x^(2n)+10x^n+16$

$= y^2+10y+16$

$= (y+2)(y+8)$

$= (x^n+2)(x^n+8)$

How do you factor x^(2n) + 10xn + 16x^(2n) + 10xn + 16?