Question

Writing: How can you tell that
x^2−19x+90
is not a perfect square trinomial?

Answer 1

because 90 is not a perfect square
(a-b)^2 = a^2 - 2ab + b^2

Answer 2

Perfect square trinomials be expressed in squared binomial form as:

( a x ± b )² = ( a x ± b ) ( a x ± b )

In this case:

x² - 19 x + 90 = ( x - 9 ) ( x - 10 )

It's not a perfect square because the members in parentheses are different.

For example:

x² - 18 x + 81 = ( x - 9 ) ( x - 9 ) = ( x - 9 )²

is a perfect square

and

x² - 20 x + 100 = ( x - 10 ) ( x - 10 ) = ( x - 10 )²

is a also perfect square