Question

Could someone please help? specifically with 1a?

Answer 1

Pair up the terms into separate groups. Then factor each group individually (pull out the GCF). Once that is finished, you factor out the overall GCF to complete the full factorization.

8r^3 - 64r^2 + r - 8
(8r^3 - 64r^2) + (r - 8)
8r^2(r - 8) + (r - 8)
8r^2(r - 8) + 1(r - 8)
(8r^2 + 1)(r - 8)

So the final answer is (8r^2 + 1)(r - 8)
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Edit:

Problem 1b) Follow the same basic steps as in part A

28v^3 + 16v^2 - 21v - 12
(28v^3 + 16v^2) + (-21v - 12)
4v^2(7v + 4) + (-21v - 12)
4v^2(7v + 4) - 3(7v + 4)
(4v^2 - 3)(7v + 4)

The answer to part B is (4v^2 - 3)(7v + 4)

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Second Edit:

I apologize for the first edit. I misread what you were asking initially. Here is problem 2A. We follow the same basic steps as in 1a) and 1b). You'll need to rearrange terms first

27mz - 12nc + 9mc - 36nz
27mz + 9mc - 12nc - 36nz
(27mz + 9mc) + (-12nc - 36nz)
9m(3z + c) + (-12nc - 36nz)
9m(3z + c) -12n(c + 3z)
9m(3z + c) -12n(3z + c)
(9m - 12n)(3z + c)
3(3m - 4n)(3z + c)