Answer :

Let's divide equation 1 into two groups.

[tex]12r^3+30r^2-10r-25\Rightarrow(12r^3+30r^2)-(10r+25)[/tex]

We now have two groups and these are (12r³ + 30r²) and (10r + 25).

For the first group, factor out 6r². It becomes 6r²(2r + 5).

For the second group, factor out 5. It becomes 5(2r + 5).

So, the entire equation can be written as:

[tex](6r^2)(2r+5)-(5)(2r+5)[/tex]

As we can see above, 2r - 5 is a common term on both groups, hence, we can rewrite the equation again as:

[tex](2r+5)(6r^2-5)[/tex]

Since 6r² - 5 cannot be factored further, the factors of equation 1 are (2r + 5)(6r² - 5).

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