Factor completely. -24x^(2)y^(3)+36x^(3)y^(4)z^(3) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms -24x^(2)y^(3) and 36x^(3)y^(4)z^(3). The GCF of the coefficients (24 and 36) is 12. The GCF of the x terms (x^2 and x^3) is x^2. The GCF of the y terms (y^3 and y^4) is y^3. There is no z term in the first expression, so z is not part of the GCF. The GCF is 12x^2y^3.Factor out GCF: Factor out the GCF from each term in the expression. -24x^(2)y^(3) + 36x^(3)y^(4)z^(3) = 12x^2y^3(-2 + 3xy^1z^3).Check for Simplification: Check if the factored expression can be simplified further. The expression inside the parentheses (-2 + 3xy^1z^3) cannot be factored further since there is no common factor between the terms.Write Final Expression: Write down the final factored expression. The completely factored form of the expression is 12x^2y^3(-2 + 3xyz^3).

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Q. Factor completely.

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-24 x^{2} y^{3}+36 x^{3} y^{4} z^{3}

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms $-24x^{2}y^{3}$ and $36x^{3}y^{4}z^{3}$ . The GCF of the coefficients ( $24$ and $36$ ) is $12$ . The GCF of the $x$ terms ( $x^2$ and $x^3$ ) is $x^2$ . The GCF of the $y$ terms ( $36x^{3}y^{4}z^{3}$ $0$ and $36x^{3}y^{4}z^{3}$ $1$ ) is $36x^{3}y^{4}z^{3}$ $0$ . There is no $36x^{3}y^{4}z^{3}$ $3$ term in the first expression, so $36x^{3}y^{4}z^{3}$ $3$ is not part of the GCF. The GCF is $36x^{3}y^{4}z^{3}$ $5$ .
Factor out GCF: Factor out the GCF from each term in the expression. $\newline$ $-24x^{2}y^{3} + 36x^{3}y^{4}z^{3} = 12x^2y^3(-2 + 3xy^1z^3)$ .
Check for Simplification: Check if the factored expression can be simplified further. $\newline$ The expression inside the parentheses $-2 + 3xy^1z^3$ cannot be factored further since there is no common factor between the terms.
Write Final Expression: Write down the final factored expression. $\newline$ The completely factored form of the expression is $12x^2y^3(-2 + 3xyz^3)$ .