Hi Michele,

All the signs in the expression 6x²+19x+3 are positive and hence if you can factor it you will have

6x²+19x+3 = (ax + b)(cx + d)

for some integers a, b, c and d.

Since the only factorization of 3 is 3 × 1, b and d are 1 and 3 or 3 and 1 so you are looking for a and c so that

6x²+19x+3 = (ax + 1)(cx + 3)

6 can be factored as 6 = 3 × 2 or 6 = 6 × 1 so the only possibilities for a and c are

a = 3, c = 2
a = 2, c = 3
a = 6, c = 1
a = 1, c = 6

For each possibility expand (ax + 1)(cx + 3) and see if any of them yield 6x²+19x+3.

Penny