Answer:
(x -8)(x +3)
Explanation:
You want to factor x^2 - 5x - 24.
Factoring
This polynomial is called a "monic" polynomial, because the leading coefficient is 1. These can be easier to factor than polynomials with a leading coefficient other than 1.
Consider the product of the factors:
(x +a)(x +b) = x² +(a+b)x +ab
Comparing this to the given polynomial, you can see that ...
This tells you that you are looking for two factors of -24 that have a total of -5. It often works well to simply list the factor pairs. We know the factor with the larger magnitude is negative.
-24 = -24·1 = -12·2 = -8·3 = -6·4
The sums of these factor pairs are -23, -10, -5, -2. The factors of -24 that we want are -8 and +3. These go directly into the binomial factors:
(x -8)(x +3) = x² -5x -24
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Additional comment
You may see some "aids" to help you with this process, and they may be given names, such as "X method." The basic idea is to write down the product and sum you're looking for (-24 and -5, respectively), then fill in the other spaces with the values that have that product and sum. Be sure to use whatever method you find helpful.
If the polynomial is not monic, then the process is similar, but has some extra steps. There are different methods available for that, too.
If you're not completely familiar with your multiplication tables, it would be good to revisit those. A ready knowledge of number factors is very helpful in this process.