Handwritten solutions to algebra problems on factoring by grouping.

Since the user has set all options to false, I will provide the final answers for the problems shown in the image. The image displays a worksheet on "Factoring By Grouping" with 6 problems already solved. I will verify each solution and list the final factored forms.

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Problem 1:
Expression: $12a^3 - 9a^2 + 4a - 3$
Group: $(12a^3 - 9a^2) + (4a - 3)$
Factor each group: $3a^2(4a - 3) + 1(4a - 3)$
Common factor: $(4a - 3)(3a^2 + 1)$ ✔ Correct

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Problem 2:
Expression: $2p^3 + 5p^2 + 6p + 15$
Group: $(2p^3 + 5p^2) + (6p + 15)$
Factor each group: $p^2(2p + 5) + 3(2p + 5)$
Common factor: $(2p + 5)(p^2 + 3)$ ✔ Correct

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Problem 3:
Expression: $3n^3 - 4n^2 + 9n - 12$
Group: $(3n^3 - 4n^2) + (9n - 12)$
Factor each group: $n^2(3n - 4) + 3(3n - 4)$
Common factor: $(3n - 4)(n^2 + 3)$ ✔ Correct

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Problem 4:
Expression: $12n^3 + 4n^2 + 3n + 1$
Group: $(12n^3 + 4n^2) + (3n + 1)$
Factor each group: $4n^2(3n + 1) + 1(3n + 1)$
Common factor: $(3n + 1)(4n^2 + 1)$ ✔ Correct

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Problem 5:
Expression: $m^3 - m^2 + 2m - 2$
Group: $(m^3 - m^2) + (2m - 2)$
Factor each group: $m^2(m - 1) + 2(m - 1)$
Common factor: $(m - 1)(m^2 + 2)$ ✔ Correct

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Problem 6:
Expression: $5n^3 - 10n^2 + 3n - 6$
Group: $(5n^3 - 10n^2) + (3n - 6)$
Factor each group: $5n^2(n - 2) + 3(n - 2)$
Common factor: $(n - 2)(5n^2 + 3)$ ✔ Correct

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All six problems are correctly solved in the image. Here are the final factored forms:

Final Answer:
1) $(4a - 3)(3a^2 + 1)$
2) $(2p + 5)(p^2 + 3)$
3) $(3n - 4)(n^2 + 3)$
4) $(3n + 1)(4n^2 + 1)$
5) $(m - 1)(m^2 + 2)$
6) $(n - 2)(5n^2 + 3)$