Factor x^2 - 7x + 12.

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Multiple Choice

Factor x^2 - 7x + 12.

Explanation:
When factoring a quadratic with a leading coefficient of 1, you want two numbers that multiply to the constant term and add to the middle coefficient, with signs matching the middle term. For x^2 - 7x + 12, look for two numbers that multiply to 12 and add to -7. The pair -3 and -4 works: (-3) + (-4) = -7 and (-3)(-4) = 12. That gives the factorization (x-3)(x-4). You can check by expanding: x^2 - 4x - 3x + 12 = x^2 - 7x + 12. Note that (x-4)(x-3) is the same factorization in the opposite order, which is still correct. The other options don’t produce the needed sum of -7 when multiplied to 12, so they don’t factor to the given quadratic.

When factoring a quadratic with a leading coefficient of 1, you want two numbers that multiply to the constant term and add to the middle coefficient, with signs matching the middle term. For x^2 - 7x + 12, look for two numbers that multiply to 12 and add to -7. The pair -3 and -4 works: (-3) + (-4) = -7 and (-3)(-4) = 12. That gives the factorization (x-3)(x-4). You can check by expanding: x^2 - 4x - 3x + 12 = x^2 - 7x + 12. Note that (x-4)(x-3) is the same factorization in the opposite order, which is still correct. The other options don’t produce the needed sum of -7 when multiplied to 12, so they don’t factor to the given quadratic.

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