Question

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

Answer 1

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

Problem: Factor `2x^2-x-3`.

The generic form of this equation is `ax^2+bx+c`.

`a=2`
`b=-1`
`c=-3`

Multiply `a` and `c`.

`2*(-3)=-6`

Find two factors of `-6` that when added equal `-1`. The numbers `-3` and `2` fit this requirement.

Rewrite the equation so that `-3x` and `2x` replace `-1x`.

Group the first and second pairs of terms.

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

Factor `x` out of the first term.

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

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

Factor out the common term `2x-3`.

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

We can also rewrite the equation as `2x^2+2x-3x-3`.

Group the two sets of terms.

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

Factor `2x` from the first term, and `3` out of the second term.

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

Factor out the common term `x+1`.

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