What is the solution to the equation 18x^5 + 6x^4 + 12x^3 + 6x^2?

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The expression 18x5 + 6x4 + 12x3 + 6x2 can be tackled by factorization and simplification. Let’s break it down step by step:

  1. Identify the common factor: The common factor among the terms is 6x2.
  2. Factor out: By factoring out 6x2, we get:

    3. 6x2(3x3 + x2 + 2x + 1)

  3. Analyze the remaining polynomial: You can factor or simplify the polynomial (3x3 + x2 + 2x + 1) further if necessary, but it does not factor nicely into simpler polynomials. This is a cubic polynomial which might require numerical methods or graphing for specific solutions.

Thus, the expression is factored as:

6x2(3x3 + x2 + 2x + 1)

You can evaluate this expression for specific values of x to find its numerical output or study the properties of the cubic polynomial for other analyses.

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