Question

How do you factor the expression `3x^2 + 2x - 1 = 0`?

Answer 1

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

Explanation:

The rule to factorise any quadratic is to find two numbers such that

`"product" = x^2 " coefficient "xx" constant coefficient"`
`"sum" \ \ \ \ \ \ = x " coefficient"`

So for `3x^2+2x-1` we seek two numbers such that

`"product" = 3*(-1) = -3`
`"sum" \ \ \ \ \ \ = 2`

So we look at the factors of `-3`. As the product is negative one of the factors must also be negative and the other positive, We compute their sum we get

`{: ("factor1", "factor2", "sum"),(-3,1,-2), (-1,3,2) :}`

So the factors we seek are `-1` and `3`

Therefore we can factorise the quadratic as follows:

`\ \ \ \ \ 3x^2+2x-1 = 3x^2 -x + 3x -1`
`:. 3x^2+2x-1 = x(3x-1) + 3x-1`
`:. 3x^2+2x-1 = (x+1)(3x-1)`

This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.