Factor completely. 27x^(3)y^(2)z^(5)+17y^(6)z Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms in the expression 27x^(3)y^(2)z^(5) and 17y^(6)z. The GCF is the largest expression that divides both terms. In this case, the GCF is y^(2)z, since it is the highest power of y and z that is present in both terms.Factor out GCF: Factor out the GCF from the expression. We write the expression as y^(2)z times the remaining factors from each term. 27x^(3)y^(2)z^(5) + 17y^(6)z = y^(2)z(27x^(3)z^(4) + 17y^(4))Check for Factors: Check for any additional common factors or special products in the remaining expression inside the parentheses. The terms 27x^(3)z^(4) and 17y^(4) do not have any further common factors, and they do not form any special products such as a difference of squares or a perfect square trinomial.Write Final Form: Write the final factored form of the expression. The completely factored form of the expression is y^(2)z(27x^(3)z^(4) + 17y^(4)).

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Q. Factor completely.

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27 x^{3} y^{2} z^{5}+17 y^{6} z

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms in the expression $27x^{3}y^{2}z^{5}$ and $17y^{6}z$ . The GCF is the largest expression that divides both terms. In this case, the GCF is $y^{2}z$ , since it is the highest power of $y$ and $z$ that is present in both terms.
Factor out GCF: Factor out the GCF from the expression. $\newline$ We write the expression as $y^{2}z$ times the remaining factors from each term. $\newline$ $27x^{3}y^{2}z^{5} + 17y^{6}z = y^{2}z(27x^{3}z^{4} + 17y^{4})$
Check for Factors: Check for any additional common factors or special products in the remaining expression inside the parentheses. $\newline$ The terms $27x^{3}z^{4}$ and $17y^{4}$ do not have any further common factors, and they do not form any special products such as a difference of squares or a perfect square trinomial.
Write Final Form: Write the final factored form of the expression. $\newline$ The completely factored form of the expression is $y^{2}z(27x^{3}z^{4} + 17y^{4})$ .