Hi Jeff,

I am going to illustrate how to factor these expressions by factoring x² + 2x - 15.

If this expression factors then the factorization will look like

x² + 2x - 15 = (x    ?)(x    ??)

where ? and ?? are yet to be determined. If I had values for ? and ?? I could expand the right side to verify that the factorization is correct. Expanding the right side gives me x², two x terms and a constant ? × ?? which must be -15. Thus ? and ?? must have opposite signs. Since 15 can only be factored as 1 × 15 or 3 × 5 the possible factorizations of x² + 2x - 15 are

(x - 1)(x + 15)
(x + 1)(x - 15)
(x - 3)(x + 5) or
(x + 3)(x - 5)

Expand each of the possibilities to see if there is one that gives the x term as + 2x.

Penny