x^2 – 10x + 24
(x – 4)(x – 6)
To factor x^2 – 10x + 24, we need to find two numbers that multiply to 24 and add to -10. These numbers are -4 and -6, because (-4) * (-6) = 24 and (-4) + (-6) = -10.
So, we can rewrite x^2 – 10x + 24 as:
x^2 – 4x – 6x + 24
Now, we can group the first two terms and the second two terms:
(x^2 – 4x) + (-6x + 24)
We can factor out x from the first group and -6 from the second group:
x(x – 4) – 6(x – 4)
Finally, we can factor out (x – 4) from both groups:
(x – 4)(x – 6)
Therefore, the factored form of x^2 – 10x + 24 is (x – 4)(x – 6).
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