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

1 Answer
Jun 28, 2015

Answer:

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#

Explanation:

#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)#