Final answer:
To make x² + 24x + c a perfect square trinomial, the value of c is 144 and the expression can be written as (x + 12)².
Step-by-step explanation:
To write the expression x² + 24x + c as a perfect square trinomial, the middle term must be twice the product of the square root of the first term and the square root of the last term. In this case, the first term is x² and the last term is c. Therefore, the middle term is 2(x)(√c).
We can rewrite the given expression as (x + (√c)²). To find the value of c, we need to equate the middle terms: 24x = 2(x)(√c). Simplifying this equation, we have 24 = 2(√c), which leads to √c = 24/2 = 12. Finally, squaring both sides, we find that c = 144.
Thus, the value of c that makes x² + 24x + c a perfect square trinomial is 144. The expression can be written as (x + 12)².
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