For what real values of c is x^2 + 16x + c the square of a binomial? If you find more than one, then list your values separated by commas.
Need help...
recall that (x+a)^2 = a^2+2ax+a^2
You have 2a = 16
To determine the real values of c for which the expression x^2 + 16x + c is a perfect square trinomial, we can use the following method:
A perfect square trinomial is in the form (x + a)^2, where a is a constant.
Expanding (x + a)^2, we get x^2 + 2ax + a^2.
By comparing this with the given expression x^2 + 16x + c, we can see that the constant term in the perfect square trinomial is a^2.
Therefore, for x^2 + 16x + c to be a perfect square trinomial, c must be equal to a^2.
In our case, we have 16x, which corresponds to 2ax in the perfect square trinomial form. This implies that 2a = 16, or a = 8.
So, c = a^2 = 8^2 = 64.
Thus, there is only one value of c for which x^2 + 16x + c is a perfect square trinomial, and that value is 64.