Question

Find all factors of 2x^3-3x^2-2x

Answer 1

x, 2x + 1, x -2

Explanation:

We have the following expression:

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

We simplify as follows to determine the factors:

`\begin{gathered} \text{ We factor the common term:} \\ \\ x\left(2x^2-3x-2\right) \\ \\ \text{ Now we factor the following term} \\ \\ 2x^2-3x-2 \\ \\ -3x=x-4x \\ \\ 2x^2+x-4x-2 \\ \\ \left(2x^2+x\right)+\left(-4x-2\right) \\ \\ x\left(2x+1\right)-2\left(2x+1\right) \\ \\ \left(2x+1\right)\left(x-2\right) \\ \\ \text{ Therefore:} \\ \\ 2x^3-3x^2-2x=x\left(2x+1\right)\left(x-2\right) \end{gathered}`

The factors would be x, 2x + 1, x -2