Question

The graph of f(x)=x^3-2x is shown what is the degree of the polynomial?

Answer 1

The polynomial
`\(f(x) = x^3 - 2x\)` has a degree of 3, indicating it is a cubic polynomial. The highest power of the variable
`\(x\)` in the polynomial is 3.

The function
`\(f(x) = x^3 - 2x\)` is a polynomial, and the degree of a polynomial is determined by the highest power of the variable present. In this case, the highest power of
`\(x\)` is 3, which means the degree of the polynomial is 3. The term
`\(x^3\)` contributes the most significant power to the polynomial, indicating a cubic function. The degree of a polynomial is crucial in understanding its behavior, as it influences the shape and characteristics of the corresponding graph. In the graph of
`\(f(x) = x^3 - 2x\),` the cubic term dominates, leading to a characteristic cubic curve. The coefficients and exponents in the polynomial provide insights into the function's behavior, roots, and turning points. In summary, the degree of the polynomial
`\(f(x) = x^3 - 2x\)` is 3, signifying a cubic function with a graph that exhibits cubic characteristics such as one or more turning points and possibly multiple real roots.