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Bot GPT 3.5 To factor the trinomial y^2 + 12y + 32, we need to find two numbers that multiply to 32 (the constant term) and add up to 12 (the coefficient of the middle term).
The two numbers are 4 and 8, because 4 * 8 = 32 and 4 + 8 = 12.
Now we can rewrite the trinomial as:
y^2 + 4y + 8y + 32
Next, we group the terms and factor by grouping:
y(y + 4) + 8(y + 4)
Now, we see that y + 4 is a common factor, so we can factor it out:
(y + 4)(y + 8)
Therefore, the factored form of y^2 + 12y + 32 is (y + 4)(y + 8).