CPM Homework Help : CCG Problem 8-74

What is the probability that $x^2 + 7x + k$ is factorable if $0\le k\le20$ and $k$ is an integer?

Hint:

Think of all of the integer pairs that sum to $7$ . Their products are the possible values of $k$ .

Hint 2:

Since $0$ is in the set of integers, there are a total of $21$ integers.

Partial Answer:

The possible values of $k$ are $0, 6, 10,$ and $12$ .