Prove: If a is any integer and the polynomial f(x) = x 2 + ax + 1 factors (poly mod 9), then there are THREE distinct non-negative integers y less than 9 such that f(y) ≡ 0 (mod 9). Hint: If x 2 +ax+ 1 ≡ (x+b)·(x+c) (mod 9), what can you deduce about b and c? Remark: This problem is very similar to the next problem.

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.

An equation in slope-intersept form the lines that passes thought (-8,1) and is perpindicular to the y=2x-17.

Alocal hamburger shop sold a combined total of 601 hamburgers and cheeseburgers on friday. there were 51 more cheeseburgers sold than hamburgers. how many hamburgers were sold on friday? a local hamburger shop sold a combined total of hamburgers and cheeseburgers on friday. there were more cheeseburgers sold than hamburgers. how many hamburgers were sold on friday?