Final answer:
The value of 'c' that makes the trinomial x²-8x+c a perfect square trinomial is 16.
Step-by-step explanation:
The student is asked to find the value of 'c' that makes the trinomial x²-8x+c a perfect square. A perfect square trinomial is a trinomial that can be written in the form (a+b)² or (a-b)². In the context of this problem, a perfect square trinomial can be formed from the binomial (x-b)².
In this binomial, 'b' is half the coefficient of x, i.e., -8/2=-4. Substituting 'b' into the binomial we get (x-4)², which expands to x² - 8x + 16, hence 'c' must be 16 for x²-8x+c to be a perfect square trinomial.
Learn more about Perfect Square Trinomial