Question

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

n^2 − 9n + 9

Answer 1

It doesn't look to me as a perfect square

Answer 2

Perfect squares are of the form -
a^2 - 2ab +b^2

Answer 3

Here a =n, b=3
but the middle term is -9n
if it would have been -6n, the polynomial would have been a perfect square

Answer 4

no, it's not perfect square

Answer 5

You can use the determinant \(\Delta = b^2-4ac\) to determine if you have a perfect square in a quadratic of the form \(ax^2+bx+c=0\)

If \(\Delta= 0\) you have a perfect square.

Here we have \(a =1, b = -9, c = 9\) and \[\Delta = (-9)^2-4(1)(9) = 81-36 = 45\]Therefore it is not a perfect square.

Answer 6

Sorry, discriminant, not determinant...