Final answer:
To form a perfect square trinomial, each expression x² + 12x + c and x² + 9x + c' should have c and c' as the squares of half the coefficient of x, which are 36 and 20.25, respectively.
Step-by-step explanation:
The student has asked to find the value of c such that the expression forms a perfect square trinomial. A perfect square trinomial is of the form (x + a)² = x² + 2ax + a², where a is a constant. In the expression x² + 12x + c, the coefficient of the linear term is 12. To find c, we use the formula for the constant term in a perfect square trinomial, which is (1/2 * coefficient of x) squared. Therefore, c is (1/2 * 12)² = 6² = 36. Similarly, for the expression x² + 9x + c, following the same method, the value c will be (1/2 * 9)² = 4.5² = 20.25.