Basic Factoring
In factoring a basic quadratic equation such as x2 + 6x + 8 = 0, you must find two
numbers that add to b (i.e., +6 in this case) and multiply to c (+8 in this case). The
numbers +4 and +2 have the properties necessary. Consequently, (x + 4) and (x + 2) are
the two factors.
To summarize:
In factoring a quadratic of the form x2 + bx + c, look for two numbers that add to b
and multiply to c
Examples of Basic Factoring
If you have not done factoring in years or it is entirely new, you may be confused at this
point. However, the following examples and explanation of going between factored and
quadratic form should clarify most confusion.
x2 + x - 12 = 0
Find two numbers that add to +1 and multiply to -12.
Two such numbers are +4 and -3.
(x + 4)(x - 3) = 0
x = -4 or x = +3 since each value satisfies the equation (x + 4)(x - 3) = 0.
Another example:
x2 - 3x - 10 = 0
Find two numbers that add to -3 and multiply to -10.
Two such numbers are -5 and +2.
(x - 5)(x + 2) = 0
x = +5 or x = -2 since each value satisfies the equation (x - 5)(x + 2) = 0.
Another example:
x2 + 7x + 6 = 0
Find two numbers that add to +7 and multiply to +6.
Two such numbers are +6 and +1.
(x + 6)(x + 1) = 0
x = -6 or x = -1 since each value satisfies the equation (x + 6)(x + 1) = 0.