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To factor the trinomial y^2 + 4y - 21, we need to find two numbers that multiply to -21 and add up to 4. The numbers that fit these criteria are 7 and -3.
So, we rewrite the trinomial as:
y^2 + 7y - 3y - 21
Now, we can factor by grouping:
y(y + 7) - 3(y + 7)
Factor out the common factor of (y + 7):
(y - 3)(y + 7)
Therefore, the factored form of the trinomial y^2 + 4y - 21 is (y - 3)(y + 7).