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Factor the polynomial by its greatest common monomial factor.

(6x^(3)+8x^(2)-4x)/( bar(+)_(+=)^(-×))=

Factor the polynomial by its greatest common monomial factor. $\newline$ $6 x^{3}+8 x^{2}-4 x=$

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Factor sums and differences of cubes

Full solution

Q. Factor the polynomial by its greatest common monomial factor.

\newline

6 x^{3}+8 x^{2}-4 x=

Identify GCF and lowest power: Identify the greatest common factor (GCF) of the coefficients and the lowest power of $x$ that is common to all terms. $\newline$ The coefficients are $6$ , $8$ , and $-4$ . The GCF of these numbers is $2$ . $\newline$ Each term contains at least one $x$ , so the lowest power of $x$ that is common to all terms is $x^1$ . $\newline$ Therefore, the GCF of the entire polynomial is $2x$ .
Divide terms by GCF: Divide each term of the polynomial by the GCF $2x$ to find the other factor. $\newline$ $6x^3 ÷ 2x = 3x^2$ $\newline$ $8x^2 ÷ 2x = 4x$ $\newline$ $-4x ÷ 2x = -2$
Write polynomial as product: Write the original polynomial as the product of the GCF and the other factor. $\newline$ The polynomial $6x^3 + 8x^2 - 4x$ can be factored as $2x(3x^2 + 4x - 2)$ .

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