Question

Is it possible to factor `y= 2x^2 + 5x - 3`? If so, what are the factors?

Answer 1

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

Explanation:

`"using the a-c method to factor the quadratic"`

`"the factors of the product "2xx-3=-6`

`"which sum to + 5 are + 6 and - 1"`

`"split the middle term using these factors"`

`2x^2+6x-x-3larrcolor(blue)"factor by grouping"`

`=color(red)(2x)(x+3)color(red)(-1)(x+3)`

`"take out the "color(blue)"common factor "(x+3)`

`=(x+3)(color(red)(2x-1))`

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