Think of the process as multiplying two binomials in reverse.
G
Practice makes perfect
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.
x^2+19x-42
In this case we have -42. 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 positive and one negative.
Factor Constants
Product of Constants
1 and -42
-42
-1 and 42
-42
2 and -21
-42
-2 and 21
-42
3 and -14
-42
-3 and 14
-42
6 and -7
-42
-6 and 7
-42
Next, let's consider the coefficient of the linear term.
x^2+19x-42
For this term we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, 19.
Since the factor constants in the possible answer choices are 14, 2, -2, and -14, we do not need to check the first two and last two lines of the table above.
Factors
Sum of Factors
2 and -21
-19
-2 and 21
19
3 and -14
-11
-3 and 14
11
We found the factors whose product is -42 and whose sum is 19.
x^2+19x-42 ⇔ (x+2)(x-21)
The correct answer choice is G.
