Let's start by factoring out the . Then, we will factor the resulting .
Factor Out the Greatest Common Factor
The greatest common factor is a common factor of all the terms in the expression. It is the common factor with the greatest and the greatest . In this case, the greatest common factor is
x.
x3+5x2+6x x⋅x2+x⋅5x+x⋅6 x(x2+5x+6)
The result of factoring out the greatest common factor from the given expression is a with a of
1.
x(x2+5x+6)
Let's temporarily only focus on the expression in parentheses, and bring back the greatest common factor after factoring.
Factor the Quadratic Expression
To factor a quadratic expression with a leading coefficient of 1, we first need to identify the values of b and c.
General Expression:Our Expression: x2+bx+c x2+5x+6
Next, we have to find a factor pair of c = 6 whose sum is b = 5. Note that 6 is a positive number, so for the product of the factors to be positive, they must have the same sign — both positive or both negative.
Factor Pair
|
Product of Factors
|
Sum of Factors
|
1 and 6
|
6
|
7
|
-1 and -6
|
6
|
-7
|
2 and 3
|
6
|
5
|
-2 and -3
|
6
|
-5
|
The factors whose product is 6 and whose sum is 5 are 2 and 3. With this information, we can now factor the trinomial. x2+5x+6⇔(x+2)(x+3)
Before we finish, remember that we factored out the greatest common factor from the original expression. Therefore, we need to include it again.
x3+5x2+6x⇔x(x+2)(x+3)