Factor 4x^3-3.6x^2- square root of 2

Problem

4*x3−3.6*x2−√(,2)

Solution

1. Identify the expression as a cubic polynomial with coefficients 4 −3.6 and −√(,2)

2. Check for common factors among the terms. The coefficients are a mix of an integer, a terminating decimal, and an irrational number.

3. Determine if standard factoring techniques apply. There is no greatest common factor other than 1 and the expression does not fit specific patterns like the sum or difference of cubes.

4. Conclude that the expression cannot be factored further over the set of rational numbers or using simple integer-based methods.

Final Answer

4*x3−3.6*x2−√(,2)=4*x3−3.6*x2−√(,2)

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