Question

What is the value of `c` in `x^2 + 8x + c` that would make it a perfect-square trinomial?

Answer 1

If `c = 16`, then `x^2 +8x +16 =(x + 4)^2`

Explanation:

This is the process called "completing the square".

If `x^2 + bx + c` is a perfect square, then there is always the same relation ship between `b and c`

"Find half of `b` and square it" , so `c = (b/2)^2`

`x^2 +8x + (8/2)^2`

=`x^2 + 8x +4^2 = x^2+ 8x +16`

=`(x +4)^2`