Factor.

Question

3z2+4z–7

Answer 1

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).