Is #x^2+8x-16# a perfect square trinomial, and how do you factor it?

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Answer 1 · 2015-06-06T14:59:06

No, it's not a perfect square trinomial, because the sign of the constant term is negative.

Using the quadratic formula #x^2+8x-16 = 0# has roots

#x = (-8+-sqrt(8^2-(4*1*-16)))/(2*1)#

#=(-8+-sqrt(128))/2#

#=-4 +- 4sqrt(2)#

So

#x^2+8x-16 = (x+4+4sqrt(2))(x+4-4sqrt(2))#

Any perfect square trinomial must be of the form:

#a^2+-2ab+b^2 = (a+-b)^2#