What value should be added to the expression to create a perfect square? x^2 + 16x A. 64 B. 4 C. 16 D. 8

Question

What value should be added to the expression to create a perfect square?


`x^2 + 16x`
A. 64
B. 4
C. 16
D. 8

Answer 1

Let's take a look at a perfect square trinomial.


`(x+7)^2`

We can distribute this expression to get
`x^2+14x+49`.

An important relation to recognize here is that the constant is the square of half of the x value.

Now, if we wanted to add a number to
`x^2+16x` to make a perfect square trinomial, we could have the value of x and then square it.

Half of 16 is 8, and 8 squared is
`\boxed{64}`