x²-13x+42
(x-6)(X-7)
To factorize x²-13x+42, we need to find two numbers that multiply to 42 and add up to -13. We can do that by listing all of the factor pairs of 42 and looking for the pair that has a sum of -13.
1, 42
2, 21
3, 14
6, 7
The pair that we want is 6 and 7 because they have a sum of -13. Now that we have found those two numbers, we can rewrite the expression as the sum of two terms:
x² – 13x + 42 = x² – 6x – 7x + 42
Notice that we have split the -13x term into -6x and -7x. We can now factor the expression by grouping:
x² – 6x – 7x + 42
= x(x – 6) – 7(x – 6)
= (x – 7)(x – 6)
Therefore, the factorization of x²-13x+42 is (x-7)(x-6).
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