To factor x²+7x+12, we need to find two numbers that multiply to 12 and add up to 7.
First, let’s list all the factor pairs of 12:
1 x 12
2 x 6
3 x 4
Now, let’s test each pair to see which one adds up to 7:
1 + 12 = 13
2 + 6 = 8
3 + 4 = 7
Therefore, the pair that adds up to 7 is 3 and 4.
Now, we can use these two numbers to factor the expression:
x²+7x+12 = (x+3)(x+4)
Therefore, the factored form of x²+7x+12 is (x+3)(x+4).
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