8
advanced-math

Identify the perfect square trinomial:

A

x2+10x+20x^2 + 10x + 20

B

x26x+9x^2 - 6x + 9

C

x2+4x+16x^2 + 4x + 16

D

x28x16x^2 - 8x - 16

Correct Answer: B

Choice B is the correct answer. A perfect square trinomial fits the form x2±2bx+b2x^2 \pm 2bx + b^2. The constant term must be the square of half the linear coefficient.

  1. For x26x+9x^2 - 6x + 9: Half of -6 is -3. (3)2=9(-3)^2 = 9. This matches.
  2. It factors to (x3)2(x - 3)^2.

Choice A is incorrect because 52=25eq205^2 = 25 eq 20. Choice C is incorrect because 22=4eq162^2 = 4 eq 16. Choice D is incorrect because the constant term in a perfect square trinomial must be positive (a real number squared is always positive).