Final answer:The polynomial 8x2 + 2 cannot be factored into simpler polynomials with rational coefficients as it is already in simplest form, being a sum of squares which does not factor over the real number system.Explanation:The student's question centers on the task of factoring the polynomial expression8x2 + 2. This expression is interesting because it does not factor into simpler polynomials with rational coefficients, which means it cannot be broken down into the product of two binomials with integer or fractional coefficients. While it's true that sum of squares, such as this one, does not factor in the set of real numbers, the only factoring that can be done would be to factor out a common constant factor. However, since8x2and2only share the number2as a common factor and considering that sum of squares doesn't factor over the real number system, the expression8x2 + 2is considered to be already in its simplest form unless we resort to complex numbers.In conclusion, the expression does not factor in the traditional sense of factoring quadratic expressions into binomials with real coefficients....

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