1. The problem asks to create one cubic polynomial and one quartic polynomial. 2. A cubic polynomial is a polynomial of degree 3, which means the highest power of the variable is 3. An example is: $$f(x) = 2x^3 - 5x^2 + 3x - 7$$ This polynomial has terms with powers 3, 2, 1, and 0. 3. A quartic polynomial is a polynomial of degree 4, meaning the highest power of the variable is 4. An example is: $$g(x) = x^4 - 4x^3 + 6x^2 - 4x + 1$$ This polynomial has terms with powers 4, 3, 2, 1, and 0. 4. Both polynomials are fully expanded and show typical coefficients and powers for their respective degrees. Final answers: - Cubic polynomial: $$2x^3 - 5x^2 + 3x - 7$$ - Quartic polynomial: $$x^4 - 4x^3 + 6x^2 - 4x + 1$$