Question

How do you factor `2x^2-11x-21`?

Answer 1

By finding its roots and, then, factoring your function!

Using Bhaskara to find its roots:

`(11+-sqrt(11^2-4(2)(-21)))/(2*2)`
`(11+-17)/4`
`x=7`, which is the same as the factor `x-7=0`
and `x=-3/2`, which is the same as the factor `2x+3=0`

Now, you just need to reaggregate them:

`(x-7)(2x+3)`

Answer 2

`2 x^2 - 11 x - 21` can be factored as `(x - 7)(2x + 3)`, as follows:

`2x^2 - 11 x - 21` `=` `2x^2 - 14 x + 3 x - 21` `=` `(2 x^2 - 14 x) + (3 x - 21)` `=` `2 x (x - 7) + 3(x - 7)` `=` `(x - 7)(2x + 3)`