To determine the degree of a polynomial, we need to identify the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial. Let's go through the given polynomial step by step:
[tex]\[ 6x^5 - 4x^2 + 2x^6 - 3 + x \][/tex]
1. Identify the terms:
- [tex]\( 6x^5 \)[/tex]
- [tex]\( -4x^2 \)[/tex]
- [tex]\( 2x^6 \)[/tex]
- [tex]\( -3 \)[/tex]
- [tex]\( x \)[/tex]
2. Determine the degree of each term:
- The term [tex]\( 6x^5 \)[/tex] has a degree of 5.
- The term [tex]\( -4x^2 \)[/tex] has a degree of 2.
- The term [tex]\( 2x^6 \)[/tex] has a degree of 6.
- The term [tex]\( -3 \)[/tex] is a constant and has a degree of 0.
- The term [tex]\( x \)[/tex] is equivalent to [tex]\( x^1 \)[/tex], so it has a degree of 1.
3. Find the highest degree:
- Out of the degrees [tex]\( 5, 2, 6, 0, 1 \)[/tex], the highest degree is 6.
Therefore, the degree of the polynomial [tex]\( 6x^5 - 4x^2 + 2x^6 - 3 + x \)[/tex] is [tex]\(\boxed{6}\)[/tex].
