Answer :

To determine the degree of a polynomial, you need to identify the highest power of the variable [tex]\( x \)[/tex] in the polynomial. Let's break down the polynomial term by term:

[tex]\[ 4x^3 + 3x^2 + 6x + 5 \][/tex]

1. First Term: [tex]\( 4x^3 \)[/tex]
- The power of [tex]\( x \)[/tex] in this term is 3.

2. Second Term: [tex]\( 3x^2 \)[/tex]
- The power of [tex]\( x \)[/tex] in this term is 2.

3. Third Term: [tex]\( 6x \)[/tex]
- The power of [tex]\( x \)[/tex] in this term is 1.

4. Fourth Term: [tex]\( 5 \)[/tex]
- This is a constant term, so the power of [tex]\( x \)[/tex] in this term is 0.

The degree of the polynomial is the highest power of [tex]\( x \)[/tex] found in any of these terms. Among the powers we have:

- [tex]\( 3 \)[/tex]
- [tex]\( 2 \)[/tex]
- [tex]\( 1 \)[/tex]
- [tex]\( 0 \)[/tex]

The highest power is 3.

Therefore, the degree of the polynomial [tex]\( 4x^3 + 3x^2 + 6x + 5 \)[/tex] is:

C. 3