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

Question

1472 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-12T23:00:11

$(x-1)(3x^2 + 5x + 3)$

Your starting expression looks like this

$3x^3 + 2x^2 - 2x - 3$

Notice that you can group the term according to their coefficients to get

$3x^3 - 3 + 2x^2 - 2x$

Use $3$ and $2x$ as common factors for their respective terms to get

$3(x^3 - 1) + 2x * (x - 1)$

Notice that you're dealing with the difference of two cubes, for which you know that

$color(blue)(a^3 - b^3 = (a-b) * (a^2 + ab + b^2))$

In your case, you have

$x^3 - 1 = x^3 - 1^3 = (x-1) * (x^2 + x + 1)$

The expression can thus be written as

$3 * (x-1) * (x^2 + x + 1) + 2x * (x-1)$

Use $(x-1)$ as a common factor

$(x-1) * [3 * (x^2 + x + 1) + 2x]$

Finally, expand the paranthesis and group like terms to get

$(x-1) * (3x^2 + 3x + 3 + 2x) = color(green)((x-1)(3x^2 + 5x + 3))$

How do you factor 3x^3+ 2x^2 -2x-33x^3+ 2x^2 -2x-3?