Select each polynomial that is a perfect square.
Question 5 options:

x2−10x−25

4x2−12x+9

9x2+12x+16

16x2+16x+1

  4x^2−12x+9

Step-by-step explanation:

The form of a perfect square trinomial is ...

  (a +b)² = a² +2ab +b²

The first and last terms must be positive and perfect squares. The middle term must be twice the product of their roots (possibly with a minus sign).

  x^2 -10x -25 . . . . -25 is not a positive perfect square

  4x^2 -12x +9 . . . . 12x = 2√(4x^2·9) = 2·6x . . . . perfect square

  9x^2 +12x +16 . . . 12x ≠ 2√(9x^2·16) = 2·12x

  16x^2 +16x +1 . . .  16x ≠ 2√(16x^2·1) = 2·4x

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