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Bot To factor 3z^2 + 4z - 7, we need to find two numbers that multiply to -21 and add up to 4.
Let's make a list of all the factors of -21:
-1, 1, -3, 3, -7, 7, -21, 21
Out of these factors, the only pair that adds up to 4 is -3 and 7.
So we can split the middle term 4z into -3z + 7z:
3z^2 - 3z + 7z - 7
Now factor by grouping:
(3z^2 - 3z) + (7z - 7)
3z(z - 1) + 7(z - 1)
(3z + 7)(z - 1)
Therefore, the factorization of 3z^2 + 4z - 7 is (3z + 7)(z - 1).