Final answer:
The degree of the polynomial is 4.
Step-by-step explanation:
The given polynomial is f(x) = 4x - 1 + 2x^4 + 10x^3. To find the degree of a polynomial, we look for the highest power of x in the polynomial. In this case, the highest power of x is 4, so the degree of the polynomial is 4.
To find the degree of the polynomial \( f(x) = 4x - 1 + 2x^4 + 10x^3 \), follow these steps: 1. **Identify the terms of the polynomial**:
A polynomial is made up of one or more terms, which are the individual summands separated by plus or minus signs. In this case, the terms are \(4x\), \(-1\), \(2x^4\), and \(10x^3\).
2. **Identify the power of \(x\) in each term**: The power of \(x\) is the exponent applied to \(x\) in each term.
For the term \(4x\), the power of \(x\) is \(1\) (since \(x\) is the same as \(x^1\)). For the term \(-1\), there is actually no \(x\), which means its power is \(0\) (as any nonzero number to the zeroth power is \(1\)). The term \(2x^4\) has \(x\) raised to the \(4\)th power. Lastly, \(10x^3\) includes \(x\) raised to the \(3\)rd power.
3. **Identify the highest power of \(x\)**: Look at all the powers you've identified in each term and find the highest one. Here, our powers are \(1\), \(0\), \(4\), and \(3\), with the highest power being \(4\).
4. **The degree of the polynomial**: The degree of a polynomial is the highest power of the variable that appears in the polynomial. In this case, the highest power is \(4\) (from the term \(2x^4\)). Therefore, the degree of the polynomial \( f(x) = 4x - 1 + 2x^4 + 10x^3 \) is \(4\).