Factor completely: 12x^(2)-16 x-2x^(3) Answer:

Rearrange terms in descending order: First, we should rearrange the terms in descending order of the powers of x. 12x^2 - 16x - 2x^3 can be rewritten as -2x^3 + 12x^2 - 16x.Factor out greatest common factor: Next, we can factor out the greatest common factor (GCF) from each term. The GCF of -2x^3, 12x^2, and -16x is -2x. Factoring out -2x gives us -2x(x^2 - 6x + 8).Factor quadratic expression: Now, we need to factor the quadratic expression x^2 - 6x + 8. We look for two numbers that multiply to 8 and add up to -6. These numbers are -2 and -4. So, we can factor the quadratic as (x - 2)(x - 4).Combine factored terms: Finally, we combine the factored quadratic with the -2x we factored out earlier to get the completely factored form of the polynomial. The final factored form is -2x(x - 2)(x - 4).

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Q. Factor completely:

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12 x^{2}-16 x-2 x^{3}

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Answer:

Rearrange terms in descending order: First, we should rearrange the terms in descending order of the powers of $x$ . $12x^2 - 16x - 2x^3$ can be rewritten as $-2x^3 + 12x^2 - 16x$ .
Factor out greatest common factor: Next, we can factor out the greatest common factor (GCF) from each term. The GCF of $-2x^3$ , $12x^2$ , and $-16x$ is $-2x$ . Factoring out $-2x$ gives us $-2x(x^2 - 6x + 8)$ .
Factor quadratic expression: Now, we need to factor the quadratic expression $x^2 - 6x + 8$ . We look for two numbers that multiply to $8$ and add up to $-6$ . These numbers are $-2$ and $-4$ . So, we can factor the quadratic as $(x - 2)(x - 4)$ .
Combine factored terms: Finally, we combine the factored quadratic with the $-2x$ we factored out earlier to get the completely factored form of the polynomial. $\newline$ The final factored form is $-2x(x - 2)(x - 4)$ .