To factor the expression x²-10x+21, we need to find two numbers that add up to -10 and multiply to 21. These numbers are -3 and -7. Therefore, we can write:
x² – 10x + 21 = (x – 3)(x – 7)
We can check that this factorization is correct by using the distributive property of multiplication:
(x – 3)(x – 7) = x(x – 7) – 3(x – 7) = x² – 7x – 3x + 21 = x² – 10x + 21
So the factored form of x²-10x+21 is (x – 3)(x – 7).
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