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+1x−12 Next, we have to find a factor pair of c = -12 whose sum is b = 1. Note that -12 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 -12 | -12 | -11 |
-1 and 12 | -12 | 11 |
2 and -6 | -12 | -4 |
-2 and 6 | -12 | 4 |
3 and -4 | -12 | -1 |
-3 and 4 | -12 | 1 |
The factors whose product is -12 and whose sum is 1 are -3 and 4. With this information, we can now factor the trinomial. x2+1x−12⇔(x−3)(x+4) Before we finish, remember that we factored out the greatest common factor from the original expression. Therefore, we need to include it again. x3+x2−12x⇔x(x−3)(x+4)