Question

. Determine whether the polynomial is a perfect square and if it is, factor it.

n^2 – 9n + 9


is not a perfect square
is a perfect square: (n + 3)^2
is a perfect square: (n – 3)^2
is a perfect square: (n – 9)^2

Answer 1

Perfect Square Trinomials have first and last terms that are positive perfect squares. And the middle term is twice the product of the square roots of the first and third terms.

First term:

n^2

Square root = n
`\checkmark`

Third term:

9

Square root = 3
`\checkmark`

9 * 1 = 9

9 * 2 = 18

18
`\\eq`-9

Therefore it is not a perfect square trinomial.