Factor the following trinomials completely.
$y^2-7y+12$

• A. $(y+3)(y-4)$
• B. $(y-3)(y-4)$
• C. $(y+7)(y-1)$
• D. $(y-1)(y-12)$

Answer: (B)

Verified step by step guidance

1. Identify the trinomial to factor: \(y^2 - 7y + 12\).
2. Look for two numbers that multiply to the constant term \(12\) and add up to the coefficient of the middle term, which is \(-7\).
3. List the factor pairs of \(12\): \((1, 12)\), \((2, 6)\), and \((3, 4)\). Since the middle term is negative, consider pairs where both numbers are negative.
4. Check which pair of negative numbers adds to \(-7\): \(-3\) and \(-4\) multiply to \(12\) and add to \(-7\).
5. Write the factored form using these numbers: \((y - 3)(y - 4)\).