## 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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