factor polynomial by grouping 3z^3+2z-12z^2-8

3z^3+2z-12z^2-8

= 3z^3 -12Z^2 + 2z -8
= 3z^2(z-4)+2(z -4)
=(z-4)(3z^2 +2)

To factor the polynomial by grouping, follow these steps:

Step 1: Group the terms in pairs.
In this case, pair the terms that have a common factor. Group the terms 3z^3 and -12z^2 together, as well as the terms 2z and -8 together.

(3z^3 - 12z^2) + (2z - 8)

Step 2: Factor out the common factor from each pair.
From the first pair, factor out z^2:
z^2(3z - 12)

From the second pair, factor out 2:
2(z - 4)

Now, the factored expression becomes:
z^2(3z - 12) + 2(z - 4)

Step 3: Look for common factors in the resulting expression.
In this case, we can factor out a common factor of (3z - 12) from both terms:
z^2(3z - 12) + 2(z - 4) = (3z - 12)(z^2 + 2)

Therefore, the factored form of the polynomial 3z^3 + 2z - 12z^2 - 8 is (3z - 12)(z^2 + 2).