Question

Prove that n^2 − 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.

Answer 1

To prove that n^2 - 7n + 12 is nonnegative, we can factor the expression and show that both factors are nonnegative for n ≥ 3.

Step-by-step explanation:

To prove that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3, we can use the concept of factoring. We can factor the expression as (n - 3)(n - 4). Since both n - 3 and n - 4 are nonnegative for n ≥ 3, their product is also nonnegative. Therefore, n^2 - 7n + 12 is nonnegative when n ≥ 3.