Question

What value of c makes the polynomial below a perfect square?

x2 + 16x + c

c =
A. 64
B. 32
C. 4
D. 256

Answer 1

Answer: The correct option is (A). 64.

Step-by-step explanation: We are given to find the value of c that makes the following polynomial a perfect square.

`P=x^2+16x+c.`

We will be using the method of completing the square to find the value of c.

We have

`P\\\\=x^2+16x+c\\\\=x^2+2* x* 8+c\\\\=(x^2+2* x* 8+8^2)+c-8^2\\\\=(x+8)^2+c-64.`

Therefore, to make the polynomial P a perfect square, we must have

`c-64=0\\\\\Rightarrow c=64.`

Thus, the required value of c is 64.

Option (A) is CORRECT.

Answer 2

To obtain the perfect square of the polynomial, take it middle term and divide it by 2. Then, take the square of the quotient. To demonstrate:

16/2 = 8
8^2 = 64

Thus, c = 64

The answer is A.