What value in place of the question mark makes the polynomial below a perfect square trinomial x^2+24x+?

A) 24

B) 48

C) 12

D) 144

Answer D

Step-by-step explanation:

Take half of the coefficient of x: Take half of + 24, obtaining 12. Now square this 12, obtaining 144. This is the desired value. Answer D is correct.

D

Step-by-step explanation:

Perfect square trinomials can be written as (a + b) ² = a² + 2ab + b². In this case, we know that a = x so we can write this as x² + 2bx + b². Since we know that 2bx = 24x we can conclude that b = 12, so that means b² = 12 * 12 = 144.