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Factor completely: x^(2)(x^(2)+3)-x(x^(2)+3)-2(x^(2)+3) Answer:

Factor completely:\newlinex2(x2+3)−x(x2+3)−2(x2+3) x^{2}\left(x^{2}+3\right)-x\left(x^{2}+3\right)-2\left(x^{2}+3\right) \newlineAnswer:

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Factor numerical expressions using the distributive propertyright chevron icon

Full solution

Q. Factor completely:\newlinex2(x2+3)−x(x2+3)−2(x2+3) x^{2}\left(x^{2}+3\right)-x\left(x^{2}+3\right)-2\left(x^{2}+3\right) \newlineAnswer:
  1. Identify common factor: Identify the common factor in all terms.\newlineThe common factor in all terms is (x2+3)(x^{2} + 3).
  2. Factor out common factor: Factor out the common factor from each term.\newlineThe expression can be rewritten as x2+3)$x2−x−2x^{2} + 3)\$x^{2} - x - 2.
  3. Factor quadratic expression: Factor the quadratic expression.\newlineWe need to factor the quadratic x2−x−2x^{2} - x - 2. To do this, we look for two numbers that multiply to −2-2 and add up to −1-1. These numbers are −2-2 and 11.
  4. Write factored form: Write the factored form of the quadratic.\newlineThe quadratic x2−x−2x^{2} - x - 2 can be factored as (x−2)(x+1)(x - 2)(x + 1).
  5. Combine with common factor: Combine the factored quadratic with the common factor.\newlineThe completely factored form of the original expression is (x2+3)(x−2)(x+1)(x^{2} + 3)(x - 2)(x + 1).

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