Question

what is the degree of the polynomial $5x^3 + 7x + 5$

Explanation:

Step1: Recall the definition of polynomial degree

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

Step2: Identify the powers of \( x \) in each term

In the polynomial \( 5x^3 + 7x + 5 \), the terms have powers of \( x \) as follows:

• For the term \( 5x^3 \), the power of \( x \) is \( 3 \).
• For the term \( 7x \), the power of \( x \) is \( 1 \) (since \( 7x = 7x^1 \)).
• For the term \( 5 \), the power of \( x \) is \( 0 \) (since \( 5 = 5x^0 \)).

Step3: Determine the highest power

Among the powers \( 3 \), \( 1 \), and \( 0 \), the highest power is \( 3 \).

Answer:

The degree of the polynomial \( 5x^3 + 7x + 5 \) is \( 3 \), so the correct option is the one with the number \( 3 \) (assuming the option with \( 3 \) is, for example, C. 3 if we follow the visual layout, but from the given options in the display, the correct choice is the box with \( 3 \)).