Factor completely. 8x^(5)-2x Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression 8x^(5)-2x. The GCF of 8x^(5) and 2x is 2x, since 2x is the largest expression that divides both terms evenly.Factor out GCF: Factor out the GCF from the expression. We can write 8x^(5)-2x as 2x(4x^(4)-1).Check for further factoring: Check if the remaining expression inside the parentheses can be factored further. The expression 4x^(4)-1 is a difference of squares, as it can be written as (2x^(2))^2 - 1^2.Factor difference of squares: Factor the difference of squares. The factored form of a difference of squares a^2 - b^2 is (a+b)(a-b). Therefore, 4x^(4)-1 can be factored as (2x^(2)+1)(2x^(2)-1).Combine with GCF: Combine the GCF with the factored form of the expression inside the parentheses. The final factored form of the expression 8x^(5)-2x is 2x(2x^(2)+1)(2x^(2)-1).

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Q. Factor completely.

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8 x^{5}-2 x

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression $8x^{5}-2x$ . The GCF of $8x^{5}$ and $2x$ is $2x$ , since $2x$ is the largest expression that divides both terms evenly.
Factor out GCF: Factor out the GCF from the expression. $\newline$ We can write $8x^{5}-2x$ as $2x(4x^{4}-1)$ .
Check for further factoring: Check if the remaining expression inside the parentheses can be factored further. $\newline$ The expression $4x^{4}-1$ is a difference of squares, as it can be written as $(2x^{2})^2 - 1^2$ .
Factor difference of squares: Factor the difference of squares. The factored form of a difference of squares $a^2 - b^2$ is $(a+b)(a-b)$ . Therefore, $4x^{4}-1$ can be factored as $(2x^{2}+1)(2x^{2}-1)$ .
Combine with GCF: Combine the GCF with the factored form of the expression inside the parentheses. $\newline$ The final factored form of the expression $8x^{5}-2x$ is $2x(2x^{2}+1)(2x^{2}-1)$ .