Question

what is the degree of the polynomial $f(x)$ defined below? $f(x) = 3 - 10x + 5x^{4} + 5x^{2} + 8x^{7}$

Explanation:

Step1: Recall the definition of polynomial degree

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial.

Step2: Identify the exponents of each term

• For the term \(3\) (which can be written as \(3x^0\)), the exponent is \(0\).
• For the term \(-10x\) (which is \(-10x^1\)), the exponent is \(1\).
• For the term \(5x^4\), the exponent is \(4\).
• For the term \(5x^2\), the exponent is \(2\).
• For the term \(8x^7\), the exponent is \(7\).

Step3: Determine the highest exponent

Among the exponents \(0, 1, 4, 2, 7\), the highest one is \(7\).

Answer:

The degree of the polynomial \(f(x)\) is \(7\).