Question

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

Answer 1

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

Explanation:

`2x^3-3x^2-2x+3`

First, start off by factoring the first two terms.

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

Next, factor out the last two terms.

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

By doing these steps, you now have `(2x-3)` to factor out.

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

The last thing you can do is factor `(x^2-1)`.

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

Answer 2

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

Explanation:

`"note that the coefficients sum to zero"`

`2-3-2+3=0`

`rArr(x-1)" is a factor"`

`rArrcolor(red)(2x^2)(x-1)color(magenta)(+2x^2)-3x^2-2x+3`

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

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

`=color(red)(2x^2)(x-1)color(red)(-x)(x-1)color(red)(-3)(x-1)+0`

`rArr2x^3-3x^2-2x+3`

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

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