Question

Is it possible to factor `y= 6x^2 - 27x - 15`? If so, what are the factors?

Answer 1

`y = 6x^2-27x-15 = 3(2x+1)(x-5)`

Explanation:

Separate out the common factor `3`, then factor by grouping as follows:

`y = 6x^2-27x-15`

`=3(2x^2-9x-5)`

`=3(2x^2-10x+x-5)`

`=3(2x(x-5)+1(x-5))`

`=3(2x+1)(x-5)`

Note that I found the split of the middle term `-9x = -10x + x` using an AC method: Look for a pair of factors of `AC = 2*5 = 10` which differ by `B=9`. The pair `10`, `1` works since `10xx1 = 10` and `10-1 = 9`.