How do you find the factored form of 3x^2 + 6x - 24
To find the factored form of the expression 3x^2 + 6x - 24, you need to factor out the greatest common factor (if it exists) and then group and factor the remaining terms.
Step 1: Factor out the greatest common factor:
The greatest common factor of all the terms is 3, so divide each term by 3:
3x^2/3 + 6x/3 - 24/3 = x^2 + 2x - 8
Step 2: Group and factor the remaining terms:
x^2 + 2x - 8 can be factored by grouping. Split the middle term (2x) into two terms such that the sum of the two terms is equal to the coefficient of the linear term (2x) and the product of the two terms is equal to the product of the first and last terms (x^2 * -8).
x^2 + 4x - 2x - 8
Now, group the terms:
(x^2 + 4x) - (2x + 8)
Factor out the common factor from each group:
x(x + 4) - 2(x + 4)
Now, notice that (x + 4) is a common factor in both terms.
(x + 4)(x - 2)
Therefore, the factored form of 3x^2 + 6x - 24 is (x + 4)(x - 2).