Let's start by factoring out the greatest common factor. Then, we will factor the resulting trinomial.
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 x2−2x−24 Next, we have to find a factor pair of c = -24 whose sum is b = -2. Note that -24 is a negative number, so for the product of the factors to be negative, they must have opposite signs — one positive and one negative.
Factor Pair | Product of Factors | Sum of Factors |
---|---|---|
1 and -24 | -24 | -23 |
-1 and 24 | -24 | 23 |
2 and -12 | -24 | -10 |
-2 and 12 | -24 | 10 |
3 and -8 | -24 | -5 |
-3 and 8 | -24 | 5 |
4 and -6 | -24 | -2 |
-4 and 6 | -24 | 2 |
The factors whose product is -24 and whose sum is -2 are 4 and -6. With this information, we can now factor the trinomial. x2−2x−24⇔(x+4)(x−6) Before we finish, remember that we factored out the greatest common factor from the original expression. Therefore, we need to include it again. x3−2x2−24x⇔x(x+4)(x−6)