Final answer:
The polynomial f(x)=5x^8+9x^6-2x^4+x^2-8 has five terms. Each term is identified by a coefficient and exponent, and they are crucial for determining the shape of the graph when graphing the polynomial.
Step-by-step explanation:
The question asks about the number of terms in the polynomial f(x)=5x8+9x6-2x4+x2-8. Counting each term that has a coefficient followed by an exponent or the constant at the end, we can easily identify that there are five terms in this polynomial. Terms in a polynomial are separated by plus or minus signs and can include variables raised to a power (like x2) or constants (like -8).
When analyzing or graphing polynomials, it's important to understand the individual components, such as the number of terms, as they impact the overall shape of the graph. You can use resources like the Equation Grapher to learn more about how these terms affect the polynomial's curve. Simplifying algebra involves eliminating terms wherever possible to make expressions more manageable, and always remember to check if the answer is reasonable by analyzing the result and looking for any mistakes.