Factor completely. 36x^(2)y^(4)z^(5)+3xyz^(4) Answer:

Find GCF: To factor the expression completely, we first look for the greatest common factor (GCF) of the two terms 36x^(2)y^(4)z^(5) and 3xyz^(4).Divide by GCF: The GCF of 36x^(2)y^(4)z^(5) and 3xyz^(4) is 3xyz^(4) because 3 is the largest integer that divides both 36 and 3, x is the highest power of x that divides both x^(2) and x, y is the highest power of y that divides both y^(4) and y, and z^(4) is the highest power of z that divides both z^(5) and z^(4).Write as Product: We divide each term by the GCF to find the other factor. 36x^(2)y^(4)z^(5) ÷ 3xyz^(4) = 12xy^(3)z and 3xyz^(4) ÷ 3xyz^(4) = 1.Check Factored Expression: Now we can write the original expression as the product of the GCF and the other factor. 36x^(2)y^(4)z^(5)+3xyz^(4) = 3xyz^(4)(12xy^(3)z + 1).We check to ensure that the factored expression, when expanded, gives us the original expression. 3xyz^(4)(12xy^(3)z + 1) = 36x^(2)y^(4)z^(5) + 3xyz^(4).

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Q. Factor completely.

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36 x^{2} y^{4} z^{5}+3 x y z^{4}

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Answer:

Find GCF: To factor the expression completely, we first look for the greatest common factor (GCF) of the two terms $36x^{2}y^{4}z^{5}$ and $3xyz^{4}$ .
Divide by GCF: The GCF of $36x^{2}y^{4}z^{5}$ and $3xyz^{4}$ is $3xyz^{4}$ because $3$ is the largest integer that divides both $36$ and $3$ , $x$ is the highest power of $x$ that divides both $x^{2}$ and $x$ , $3xyz^{4}$ $0$ is the highest power of $3xyz^{4}$ $0$ that divides both $3xyz^{4}$ $2$ and $3xyz^{4}$ $0$ , and $3xyz^{4}$ $4$ is the highest power of $3xyz^{4}$ $5$ that divides both $3xyz^{4}$ $6$ and $3xyz^{4}$ $4$ .
Write as Product: We divide each term by the GCF to find the other factor. $\newline$ $36x^{2}y^{4}z^{5} \div 3xyz^{4} = 12xy^{3}z$ and $3xyz^{4} \div 3xyz^{4} = 1$ .
Check Factored Expression: Now we can write the original expression as the product of the GCF and the other factor. $36x^{2}y^{4}z^{5}+3xyz^{4} = 3xyz^{4}(12xy^{3}z + 1)$ .
Check Factored Expression: Now we can write the original expression as the product of the GCF and the other factor. $\newline$ $36x^{2}y^{4}z^{5}+3xyz^{4} = 3xyz^{4}(12xy^{3}z + 1)$ .We check to ensure that the factored expression, when expanded, gives us the original expression. $\newline$ $3xyz^{4}(12xy^{3}z + 1) = 36x^{2}y^{4}z^{5} + 3xyz^{4}$ .