Factoring a Trinomial of the Form x2+ bx+ c
To factor a trinomial of the form x2 + bx
+ c, we can use the
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).
Factor: x2 - 2x - 24
The trinomial x2 - 2x - 24 has the form
x2 + bx + c where b
= -2, and
c = -24.
||Find two integers whose product is c and whose sum is b.
We seek two integers whose product is -24 and whose sum is
Since the product, c = -24, is negative, the integers must have
Since the sum, b = 2, is negative, the integer with the greater
absolute value must be negative.
Here are some possibilities:
The integers -6 and 4 give the required product,
-24, and the
required sum, -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.
We can use FOIL to check the
|(x - 6)(x
+ 4x - 6x -
= x2 -
2x - 24
The factorization checks.