Factor: x2 - 14x - 15
Solution: First, write down two sets of parentheses to indicate
the product.
( )( )
Since the first term in the trinomial is the product of the first terms
of the binomials, you enter x as the first term of each binomial.
(x )(x )
The product of the last terms of the binomials must equal -15,
and their sum must equal -14, and one of the binomials' terms has to be negative. Four different pairs of
factors have a product that equals -15.
(3)(-5) = -15 (-15)(1) = -15
(-3)(5) = -15
(15)(-1) = -15
However, only one of those pairs has a sum of -14.
(-15) + (1) = -14
Therefore, the second terms in the binomial are -15 and 1
because these are the only two factors whose product is -15 (the last term of the trinomial) and whose sum is
-14 (the coefficient of the middle term in the trinomial).
(x - 15)(x + 1) is the answer.
