Question

How do you factor `21r^2+32r-13`?

Answer 1

`21r^2+32r-13`

`= 21r^2-7r+39r-13`

`= (7r+13)(3r-1)`

Explanation:

The trick here is to find the split of the middle term into two numbers whose difference is `32` and whose product is `21*13 = 3*7*13 = 273`. There are not many choices of pairs of factors of `3*7*13` and we can quickly find `39` and `7`.

Then we can factor by grouping:

`21r^2+32r-13`

`= 21r^2-7r+39r-13`

`= (21r^2-7r)+(39r-13)`

`= 7r(3r-1)+13(3r-1)`

`= (7r+13)(3r-1)`