x²-13x+42
(x-6)(X-7)
To factor x²-13x+42, we need to find two numbers that multiply to 42 and add up to -13. We can start by listing all of the factor pairs for 42:
1 × 42
2 × 21
3 × 14
6 × 7
Out of these factor pairs, 6 and 7 are the only ones that have a difference of -1 (since we need two numbers that add up to -13).
So, we can rewrite -13x as -6x-7x. Then, we can factor by grouping:
x²-6x-7x+42
(x²-6x)- (7x-42)
x(x-6)-7(x-6)
(x-7)(x-6)
Therefore, x²-13x+42 can be factored as (x-7)(x-6).
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