## Precalculus: Mathematics for Calculus, 7th Edition

To factor the trinomial $x^{2}$ + 7x + 10, we look for two integers whose product is 10 and whose sum is 7. These integers are 5 and 2, so the trinomial factors as (x + 5)(x + 2).
When factoring a trinomial of the form M$x^{2}$ + Nx + O, where M, N, and O are real numbers, the trinomial can be factored into two binomials of the form (Ax + B)(Cx + D), where A, B, C, and D are real numbers. If the $x^{2}$ term does not have a coefficient, then the two x terms (A and B) will have a coefficient of 1 and the constants (C and D) will be the factors of O that sum to N. In this case, we are looking for two terms whose product is 10 and whose sum is 7. The products of 10 are: 1, 2, 5, and 10, so the terms must either be 10 and 1 or 5 and 2. 5 and 2 adds to 7, therefore these are the constants.