To factor the polynomial [tex]\(2x^3 + 4x^2 - x\)[/tex], let’s break it down step by step:
1. Identify common factors: First, look for any common factors in each term of the polynomial. Here, each term contains [tex]\(x\)[/tex], so we can factor out [tex]\(x\)[/tex].
[tex]\[ 2x^3 + 4x^2 - x = x(2x^2 + 4x - 1) \][/tex]
2. Review the factorized form: After factoring out [tex]\(x\)[/tex], we are left with the polynomial [tex]\(2x^2 + 4x - 1\)[/tex] inside the parentheses.
Therefore, the factored form of [tex]\(2x^3 + 4x^2 - x\)[/tex] is:
[tex]\[ x(2x^2 + 4x - 1) \][/tex]
This matches the fourth option provided:
[tex]\[ x\left(2 x^2+4 x-1\right) \][/tex]
So, the correct answer is:
[tex]\[ x\left(2 x^2 + 4 x - 1\right) \][/tex]
