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To factor the trinomial y^2 + 12y + 32, we need to find two numbers that multiply to 32 and add up to 12. The numbers that fit these criteria are 4 and 8.
Therefore, we can rewrite the trinomial as:
y^2 + 4y + 8y + 32
Now, we can factor by grouping:
y(y + 4) + 8(y + 4)
Now we can factor out the common factor of (y + 4):
(y + 4)(y + 8)
So, the factored form of the trinomial y^2 + 12y + 32 is (y + 4)(y + 8).