Answered

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


x2 + 16x + c


c =

A64
B32
C4
D256

Verified Answer :

MissPhiladelphia

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.

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

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

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.

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