Exercise 1 Page 300

To factor a trinomial with a leading coefficient of one, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term. In this case, we have $\text{-}18.$ This is a negative number, so for the product of the constant terms in the factors to be negative, these constants must have the opposite sign (one negative and one positive.)

Factor Constants	Product of Constants
$\text{-}18$ and $1$	$\text{-}18$
$\text{-}1$ and $18$	$\text{-}18$
$\text{-}9$ and $2$	$\text{-}18$
$\text{-}2$ and $9$	$\text{-}18$
$\text{-}6$ and $3$	$\text{-}18$
$\text{-}3$ and $6$	$\text{-}18$

Next, let's consider the coefficient of the linear term. For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, $\text{-}3.$

Factors	Sum of Factors
$\text{-}18$ and $1$	$\text{-}17$
$\text{-}1$ and $18$	$17$
$\text{-}9$ and $2$	$\text{-}7$
$\text{-}2$ and $9$	$7$
$\text{-}6$ and $3$	$\text{-}3$
$\text{-}3$ and $6$	$3$

We found the factors whose product is $\text{-}18$ and whose sum is $\text{-}3.$