How do you determine whether #x^2-8x+81# is a perfect square trinomial?

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Answer 1 · 2017-08-15T11:52:05

#x^2 -8x +81# is not a perfect square trinomial.

#x^2 -18x +81# is a perfect square trinomial.

If you square a binomial, there is always a pattern which emerges:

In #ax^2 +bx +c#:

If #a = 1#, then in a perfect square trinomial #c = (b/2)^2#

Check to see if 'half of #b#', squared, is equal to #c#

In #x^2 -8x+81" "rarr ((-8)/2)^2 = 16#

#16 != 81# so it is not a perfect square trinomial.

[Compare with #x^2 -18x+81#, where #((-18)/2)^2 = 81#]
This would give:

#x^2 -18x +81 = (x-9)^2#