x^2 – 11x + 24
(x – 3)(x – 8)
To factor x^2 – 11x + 24, we need to find two numbers whose sum is -11 and whose product is (1)(24) = 24. These numbers are -3 and -8 (since -3 + (-8) = -11 and (-3)(-8) = 24).
Now we can rewrite x^2 – 11x + 24 as
x^2 – 3x – 8x + 24
Next, we group the terms, taking the common factors out of each group:
(x^2 – 3x) – (8x – 24)
Now we can factor each group separately:
x(x – 3) – 8(x – 3)
Notice that we have a common factor of (x – 3), which we can factor out:
(x – 3)(x – 8)
Therefore, x^2 – 11x + 24 factors as (x – 3)(x – 8).
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