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
