Question

factor the trinomial.
$c^2 + 4c + 77$
select the correct choice below and fill in any answer boxes within your choice.
a. the answer is

b. the trinomial is not factorable.

Explanation:

Step1: Recall factoring trinomial

For a trinomial \(ax^2 + bx + c\) (here \(a = 1\), \(b = 4\), \(c = 77\)), we need two numbers that multiply to \(ac=77\) and add to \(b = 4\).

Step2: Find factors of 77

Factors of 77: \(1\times77 = 77\), \(7\times11 = 77\). Check sums: \(1 + 77 = 78\), \(7+11 = 18\). Neither sum is 4. So no such real numbers exist for factoring.

Answer:

B. The trinomial is not factorable.