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

2 Answers
Jul 4, 2017

(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)

Jul 4, 2017

(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)