Final answer:
The value of C that makes the expression x^2 - 6x + c a perfect square trinomial is 9. The expression can then be written as the square of a binomial, which is (x - 3)^2.
Step-by-step explanation:
To find the value of C that makes the expression x^2 - 6x + c a perfect square trinomial, we need to use the formula for creating a perfect square. A perfect square trinomial is in the form (x - a)^2 = x^2 - 2ax + a^2, where 2a is the coefficient of the x-term in our trinomial, which in this case is -6. Therefore, a is -6/2 = -3.
We then square the value of a to get the constant term c. So, c = (-3)^2 = 9.
Therefore, the value of c that makes the expression a perfect square trinomial is 9, and the expression can be written as the square of a binomial, which is (x - 3)^2.