Question

question 4 of 25
what value of c makes the polynomial below a perfect square?
$x^2 + 16x + c$
$c = $

a. 256
b. 4
c. 32
d. 64

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial has the form \( (x + a)^2 = x^2 + 2ax + a^2 \). For the given polynomial \( x^2 + 16x + c \), we compare it with \( x^2 + 2ax + a^2 \). Here, \( 2a = 16 \).

Step2: Solve for \( a \)

From \( 2a = 16 \), we divide both sides by 2: \( a=\frac{16}{2}=8 \).

Step3: Find \( c \)

Since \( c = a^2 \), substitute \( a = 8 \) into the formula: \( c = 8^2 = 64 \).

Answer:

D. 64