Factor completely: 4x^(2)(x-4)-(x-4) Answer:

Identify common factor: Identify the common factor in both terms of the expression. The common factor is (x-4).Factor out common factor: Factor out the common factor from the expression. The expression 4x^2(x-4) - (x-4) can be written as (x-4)(4x^2 - 1).Recognize difference of squares: Recognize that the expression 4x^2 - 1 is a difference of squares. A difference of squares can be factored as (a^2 - b^2) = (a + b)(a - b). Here, a = 2x and b = 1, so 4x^2 - 1 = (2x)^2 - 1^2.Factor difference of squares: Factor the difference of squares. Using the identity from the previous step, we get (2x + 1)(2x - 1).Combine factored parts: Combine the factored parts to get the final factored expression. The completely factored form is (x-4)(2x + 1)(2x - 1).

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Q. Factor completely:

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4 x^{2}(x-4)-(x-4)

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Answer:

Identify common factor: Identify the common factor in both terms of the expression. $\newline$ The common factor is $(x-4)$ .
Factor out common factor: Factor out the common factor from the expression. $\newline$ The expression $4x^2(x-4) - (x-4)$ can be written as $(x-4)(4x^2 - 1)$ .
Recognize difference of squares: Recognize that the expression $4x^2 - 1$ is a difference of squares. $\newline$ A difference of squares can be factored as $(a^2 - b^2) = (a + b)(a - b)$ . $\newline$ Here, $a = 2x$ and $b = 1$ , so $4x^2 - 1 = (2x)^2 - 1^2$ .
Factor difference of squares: Factor the difference of squares. $\newline$ Using the identity from the previous step, we get $(2x + 1)(2x - 1)$ .
Combine factored parts: Combine the factored parts to get the final factored expression. $\newline$ The completely factored form is $(x-4)(2x + 1)(2x - 1)$ .