Reading the Product

In the last section you expanded (x + 2)(x + 3) and got x^2 + 5x + 6. Look at the two numbers 2 and 3. The middle coefficient 5 is their sum, 2 + 3. The constant 6 is their product, 2 × 3. The two cross products make the middle term, and the two last terms make the constant.

To factor x^2 + bx + c, find two numbers p and q with p + q = b and pq = c. Then x^2 + bx + c = (x + p)(x + q).

To factor x^2 + 5x + 6, find two numbers with sum 5 and product 6. The pair is 2 and 3, so the factored form is (x + 2)(x + 3). To check, expand the product and compare it with the original trinomial.