Factoring Trinomials
Factoring a Trinomial of the Form x^{2}+ bx+ c
To factor a trinomial of the form x^{2} + bx
+ c, we can use the
productsum method.
Procedure â€”
To Factor x^{2}+ bx+ c Using the ProductSum Method
Step 1 Find two integers whose product is c and whose sum is b.
Step 2 Substitute the integers from Step 1 for the constants, r and s,
in the binomial factors (x + r) and (x + s).
Example 1
Factor: x^{2}  2x  24
Solution
The trinomial x^{2}  2x  24 has the form
x^{2} + bx + c where b
= 2, and
c = 24.
Step 1

Find two integers whose product is c and whose sum is b.
We seek two integers whose product is 24 and whose sum is
2.
Since the product, c = 24, is negative, the integers must have
opposite signs.
Since the sum, b = 2, is negative, the integer with the greater
absolute value must be negative.
Here are some possibilities:
Product
24
Â· 1
12
Â· 2
8
Â· 3
6
Â· 4 
Sum
23
10
5
2 
The integers 6 and 4 give the required product,
24, and the
required sum, 2. 
Step 2 
Substitute the integers from Step 1 for the constants, r and s, in
the binomial factors (x + r) and (x + s). The factorization is (x  6)(x + 4).
You can multiply to check the factorization.

Note:
We can use FOIL to check the
factorization:
(x  6)(x
+ 4) 
= x^{2}
+ 4x  6x 
24 = x^{2} 
2x  24 
The factorization checks.
