Question

How do you factor `2x^2+5x-3`?

Answer 1

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

Explanation:

The standard form of the `color(blue)"quadratic function"` is.

`y=ax^2+bx+c`

To factorise the function.

• consider the factors of the product ac which sum to give b

`"for "2x^2+5x-3`

`a=2, b=5" and "c=-3`

`rArrac=2xx-3=-6`

`"the required factors of -6 are "+6" and "-1`

`"Since " 6xx-1=-6" and " +6-1=+5`

`"now express " 2x^2+5x-3" as"`

`2x^2color(red)(+6x-x)-3`

Factorise by 'grouping'

`rArr2x(x+3)-1(x+3)`

Take out `color(blue)"common factor " "of " (x+3)`

`rArr(x+3)(2x-1)larr" in factorised form"`