x²-10x+21
(x-7)(x-3)
To factorize the quadratic expression x² – 10x + 21, we need to find two factors of 21 that add up to -10. The factors of 21 are 1, 3, 7 and 21. Among these, only 3 and 7 add up to -10. Therefore, we can write x² – 10x + 21 as:
x² – 10x + 21 = (x – 3)(x – 7)
This is the factored form of the quadratic expression. To check that this is correct, we can expand it using the distributive property:
(x – 3)(x – 7) = x(x – 7) – 3(x – 7) = x² – 7x – 3x + 21 = x² – 10x + 21
Thus, the factored form is correct.
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