Factor completely: 36x^(2)-81 x-3x^(3) Answer:

Reorder Terms in Descending Order: First, we should reorder the terms of the polynomial in descending powers of x. 36x^2 - 81x - 3x^3 can be rewritten as -3x^3 + 36x^2 - 81x.Factor Out GCF: Next, we can factor out the greatest common factor (GCF) from each term. The GCF here is -3x. Factoring out -3x gives us -3x(x^2 - 12x + 27).Factor Quadratic Expression: Now we need to factor the quadratic expression x^2 - 12x + 27. We look for two numbers that multiply to 27 and add up to -12. These numbers are -3 and -9. So, we can write x^2 - 12x + 27 as (x - 3)(x - 9).Combine Factors for Final Form: Finally, we combine the factored quadratic with the GCF we factored out earlier to get the completely factored form of the polynomial. The final factored form is -3x(x - 3)(x - 9).

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Factor completely:

36x^(2)-81 x-3x^(3)
Answer:

Factor completely: $\newline$ $36 x^{2}-81 x-3 x^{3}$ $\newline$ Answer:

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Q. Factor completely:

\newline

36 x^{2}-81 x-3 x^{3}

\newline

Answer:

Reorder Terms in Descending Order: First, we should reorder the terms of the polynomial in descending powers of $x$ . $36x^2 - 81x - 3x^3$ can be rewritten as $-3x^3 + 36x^2 - 81x$ .
Factor Out GCF: Next, we can factor out the greatest common factor (GCF) from each term. The GCF here is $-3x$ . $\newline$ Factoring out $-3x$ gives us $-3x(x^2 - 12x + 27)$ .
Factor Quadratic Expression: Now we need to factor the quadratic expression $x^2 - 12x + 27$ . We look for two numbers that multiply to $27$ and add up to $-12$ . These numbers are $-3$ and $-9$ . So, we can write $x^2 - 12x + 27$ as $(x - 3)(x - 9)$ .
Combine Factors for Final Form: Finally, we combine the factored quadratic with the GCF we factored out earlier to get the completely factored form of the polynomial. $\newline$ The final factored form is $-3x(x - 3)(x - 9)$ .