Question

what is the factored form of $2x^3 + 4x^2 - x$?
○ $2x(x^2+2x+1)$
○ $x(2x^2+4x+1)$
○ $2x(x^2+2x-1)$
○ $x(2x^2+4x-1)$

Explanation:

Step1: Identify common factor

The common term in $2x^3 + 4x^2 - x$ is $x$.

Step2: Factor out the common term

Divide each term by $x$:
$\frac{2x^3}{x} + \frac{4x^2}{x} - \frac{x}{x} = 2x^2 + 4x - 1$
Rewrite the expression with the factored out term: $x(2x^2 + 4x - 1)$

Step3: Match with options

Compare the result to the given choices.

Answer:

$x(2x^2+4x-1)$ (the last option)