x²-10x+21
(x-7)(x-3)
To factorize the expression x²-10x+21, we need to find two numbers that add up to -10 and multiply to 21. How can we do this?
Firstly, let’s list all possible pairs of factors of 21: (1,21), (3,7). We can see that 3 and 7 add up to 10, but the signs of the terms in the original expression are both negative; therefore, we need to use -3 and -7 as our numbers.
So, we can rewrite x²-10x+21 as:
x² – 3x – 7x + 21
Now we group the terms with a common factor:
(x² -3x) + (-7x + 21)
We can factor out x from the first group and -7 from the second group:
x(x – 3) – 7(x – 3)
And we can see that both terms have a common factor of (x – 3):
(x – 3)(x – 7)
Therefore, the expression x² – 10x + 21 factors to (x – 3)(x – 7).
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