Answer:
To factorize the quadratic expression x² - 10x + 24, we need to find two numbers that multiply to give the coefficient of the constant term (24) and add up to give the coefficient of the linear term (-10).
Let's look for two numbers that meet these criteria:
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
Now, we need to find a pair of numbers from these factors that add up to -10. The pair that satisfies this is -6 and -4, because -6 + (-4) = -10.
So, we can rewrite the middle term (-10x) using these two numbers:
x² - 6x - 4x + 24
Now, we can group the terms and factor by grouping:
x(x - 6) - 4(x - 6)
Notice that we have a common factor of (x - 6) in both terms. We can factor it out:
(x - 6)(x - 4)
Therefore, the factored form of the quadratic expression x² - 10x + 24 is (x - 6)(x - 4).