a) \( F(x)=(x+2 y) \) b) \( F(x)=(30+27) \) c) \( F(x)=x^{3} \) d) \( F(x)=5 x^{3}+2 x \) e) \( F(x)=5 x^{3}+3 x^{2}-6 x+6 \) f) \( F(x)=2 x^{2} / 3 \)

Did you know that polynomials like \( F(x) = 5x^3 + 3x^2 - 6x + 6 \) can model a variety of real-world situations, from predicting profits in business to describing the motion of a vehicle? These functions, specifically polynomials, can help you understand trends and make forecasts based on input values. When working with polynomials, one common mistake is forgetting to combine like terms, which can lead to incorrect expressions and results. It's crucial to double-check and simplify your polynomial fully before proceeding with calculations or graphing, ensuring your mathematical representations are clear and accurate!