Factor the trinomial x2 - 5x - 14?

Answer 1

Since we're working with a degree two polynomial, we can see fairly quickly that the factorization will be some form of (x + a)(x + b). So the question boils down to, how do we know what a and b are?

We start with the factors of our constant, 14, which are 1, 2, 7, and 14. Based on the second term, we know that the difference between these factors is 5, so the best candidates for a and b would be 2 and 7.

We also know that the constant is negative, which means that either a or b must be negative. Based on the fact that the coefficient of the second term is negative, it follows that the larger number is the negative one. So our a and b are 2 and -7, which makes the factorization (x + 2)(x - 7).