Think of the process as multiplying two binomials in reverse.
(k+3)(k-8)
Practice makes perfect
To factor a trinomial with a leading coefficient of one, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term.
k^2-5k - 24
In this case, we have - 24. This is a negative number, so for the product of the constant terms in the factors to be negative, these constants must have the opposite sign (one positive and one negative).
Factor Constants
Product of Constants
1 and - 24
- 24
- 1 and 24
- 24
2 and - 12
- 24
- 2 and 12
- 24
3 and - 8
- 24
- 3 and 8
- 24
4 and - 6
- 24
- 4 and 6
- 24
Next, let's consider the coefficient of the linear term.
k^2 - 5k - 24
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, - 5.
Factors
Sum of Factors
1 and - 24
- 23
- 1 and 24
23
2 and - 12
- 10
- 2 and 12
10
3 and - 8
- 5
We found the factors whose product is - 24 and whose sum is - 5.
k^2 - 5k - 24 ⇔ (k+3)(k-8)
Checking Our Answer
Check your answer âś“
We can check our answer by applying the Distributive Property and comparing the result with the given expression.
After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!
