Answer:
Therefore, the factor pairs needed to answer 3z^2 + 26z - 9 are (-3, 9) and (3z - 1, z + 9).
Explanation:
To factor the quadratic expression 3z^2 + 26z - 9, we need to find two numbers that multiply to give us 3 times -9 = -27, and add up to 26.
One way to do this is to list all the factor pairs of -27 and look for the pair that has a sum of 26:
-27 and 1
-9 and 3
-3 and 9
-1 and 27
We can see that the pair that adds up to 26 is -3 and 9. So we can use these numbers to write the quadratic expression as a product of two binomials:
3z^2 + 26z - 9 = (3z - 1)(z + 9)
Therefore, the factor pairs needed to answer 3z^2 + 26z - 9 are (-3, 9) and (3z - 1, z + 9).