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What is the factored form of [tex]2x^3 + 4x^2 - x[/tex]?

A. [tex]2x(x^2 + 2x + 1)[/tex]
B. [tex]x(2x^2 + 4x + 1)[/tex]
C. [tex]2x(x^2 + 2x - 1)[/tex]
D. [tex]x(2x^2 + 4x - 1)[/tex]

Sagot :

GinnyAnsweridn
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]
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