1. **State the problem:** Determine if the expression $6x^2 + 2x^4 - 8$ is a polynomial and if so, write it in standard form. 2. **Recall the definition of a polynomial:** A polynomial is an algebraic expression consisting of terms with non-negative integer exponents of the variable and coefficients that are real numbers. 3. **Check each term:** - $6x^2$ has exponent 2 (non-negative integer), coefficient 6 (real number). - $2x^4$ has exponent 4 (non-negative integer), coefficient 2 (real number). - $-8$ is a constant term (can be considered as $-8x^0$ with exponent 0). All terms satisfy the polynomial criteria. 4. **Write the polynomial in standard form:** Standard form orders terms from highest to lowest exponent. The highest exponent is 4, so the standard form is: $$2x^4 + 6x^2 - 8$$ 5. **Final answer:** Yes, the expression is a polynomial and its standard form is $2x^4 + 6x^2 - 8$.