Factories k^2-5k-24 completely .show your working

Answer 1

To factor the quadratic expression \(k^2 - 5k - 24\), we need to find two numbers that multiply to -24 and add up to -5.

Let's list the factors of -24:

1, -24
-1, 24
2, -12
-2, 12
3, -8
-3, 8
4, -6
-4, 6

From the list, we can see that -8 and 3 are two numbers that multiply to -24 and add up to -5.

Therefore, we can rewrite the expression as:
\(k^2 - 8k + 3k - 24\)

Now, let's factor by grouping:
\(k(k - 8) + 3(k - 8)\)

Now, we have a common binomial factor of \(k - 8\):
\((k + 3)(k - 8)\)

So, the fully factored expression is \( (k + 3)(k - 8) \).