To find the degree of the polynomial \( 6x^5 - 4x^2 + 2x^3 - 3 + x \), we identify the term with the highest power of \( x \).
The terms of the polynomial are:
- \( 6x^5 \) (degree 5)
- \( -4x^2 \) (degree 2)
- \( 2x^3 \) (degree 3)
- \( -3 \) (degree 0, constant term)
- \( x \) (degree 1)
The term with the highest degree is \( 6x^5 \), which has a degree of 5.
Therefore, the degree of the polynomial \( 6x^5 - 4x^2 + 2x^3 - 3 + x \) is \( 5 \).