x²+7x+12
(x+3)(x+4)
To factor the quadratic expression x²+7x+12, we need to find two numbers that multiply together to give 12 and add together to give 7. These two numbers are 3 and 4, because 3×4=12 and 3+4=7. Therefore, we can write the expression as:
x²+7x+12 = (x+3)(x+4)
This is the factored form of the quadratic expression. We can check this by using the distributive property of multiplication:
(x+3)(x+4) = x(x+4) + 3(x+4) = x²+4x+3x+12 = x²+7x+12
Therefore, (x+3)(x+4) is the correct factorization of x²+7x+12.
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