Problem 40

Question

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$6 x-4 x^{2}+2 x^{3}$$

Step-by-Step Solution

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Answer

The factored form of the polynomial $6x - 4x^{2} + 2x^{3}$ is $2x(3 - 2x + x^{2})$.

1Step 1: Identify the Greatest Common Factor

For $6x$, $-4x^{2}$, and $2x^{3}$, each term has a common factor of $2x$.

2Step 2: Factor out the Greatest Common Factor

The polynomial $6x - 4x^{2} + 2x^{3}$ can be rewritten by factoring out the greatest common factor of $2x$ from each term: $2x(3 - 2x + x^{2})$.

3Step 3: Simplify the Resulting Expression

Already the polynomial is simplified; hence no further simplification is required.

Problem 40

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