Identify Common Factor: Identify if there is a common factor in all terms of the polynomial 2x^(3)+32x^(2)+128x. The common factor is 2x, as each term is divisible by 2x.Factor Out Common Factor: Factor out the common factor 2x from each term of the polynomial. 2x(x^2 + 16x + 64)Check Quadratic Factorization: Check if the quadratic x^2 + 16x + 64 can be factored further. The quadratic is a perfect square trinomial because (8x)^2 = 64x^2, 2 * 8x * 8 = 128x, and 8^2 = 64.Factor Quadratic: Factor the quadratic x^2 + 16x + 64 into (x + 8)^2. 2x(x + 8)^2Check Further Simplification: Check for any further simplification. No further simplification is possible.

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$2 x^{3}+32 x^{2}+128 x$

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2 x^{3}+32 x^{2}+128 x

Identify Common Factor: Identify if there is a common factor in all terms of the polynomial $2x^{3}+32x^{2}+128x$ . The common factor is $2x$ , as each term is divisible by $2x$ .
Factor Out Common Factor: Factor out the common factor $2x$ from each term of the polynomial. $2x(x^2 + 16x + 64)$
Check Quadratic Factorization: Check if the quadratic $x^2 + 16x + 64$ can be factored further. $\newline$ The quadratic is a perfect square trinomial because $(8x)^2 = 64x^2$ , $2 \times 8x \times 8 = 128x$ , and $8^2 = 64$ .
Factor Quadratic: Factor the quadratic $x^2 + 16x + 64$ into $(x + 8)^2$ . $\newline$ $2x(x + 8)^2$
Check Further Simplification: Check for any further simplification. $\newline$ No further simplification is possible.