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Factor the expression completely. 5x^(3)-2x Answer:

Factor the expression completely.\newline5x3−2x 5 x^{3}-2 x \newlineAnswer:

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Full solution

Q. Factor the expression completely.\newline5x3−2x 5 x^{3}-2 x \newlineAnswer:
  1. Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression.\newlineThe terms 5x35x^3 and 2x2x both have xx as a common factor. The greatest power of xx that divides both terms is x1x^1 (or simply xx).
  2. Factor Out GCF: Factor out the GCF from each term in the expression.\newlineThe expression 5x3−2x5x^3 - 2x can be factored by taking out the common factor xx:\newlinex(5x2−2)x(5x^2 - 2)
  3. Check Further Factoring: Check if the remaining expression inside the parentheses can be factored further.\newlineThe expression 5x2−25x^2 - 2 is a difference of two terms that are not a difference of squares or any other factorable form. Therefore, it cannot be factored further.
  4. Write Completely Factored Form: Write down the completely factored form of the original expression.\newlineThe completely factored form of the expression 5x3−2x5x^3 - 2x is x(5x2−2)x(5x^2 - 2).

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