Question

Factor the expression using grouping, equation 1.1.12r^3 + 30r^2 - 10r - 252.5x^3 + 15^2 + 6x + 18

Answer 1

Let's divide equation 1 into two groups.

`12r^3+30r^2-10r-25\Rightarrow(12r^3+30r^2)-(10r+25)`

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:

`(6r^2)(2r+5)-(5)(2r+5)`

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

`(2r+5)(6r^2-5)`

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