Factoring Trinomials
Factoring a Trinomial of the Form x2+ bx+ c
To factor a trinomial of the form x2 + bx
+ c, we can use the
product-sum method.
Procedure —
To Factor x2+ bx+ c Using the Product-Sum 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: x2 - 2x - 24
Solution
The trinomial x2 - 2x - 24 has the form
x2 + 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
· 1
-12
· 2
-8
· 3
-6
· 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) |
= x2
+ 4x - 6x -
24 = x2 -
2x - 24 |
The factorization checks.
|
