A fourth degree polynomial has a fourth power of the variable (e.g., x^4 or ax^4 where a is a constant). There may be lower powers of the variable and a fourth degree polynomial would have no more than 5 terms including the constant after the coefficient of the each power of the variable has been consolidated (added/subtracted).
Example: 2x^4+6x-x^3-5x^2+7+3x-1 when consolidated is 2x^4-x^3-5x^2+9x+6.
The given polynomial is of degree one: x+5 because the other x's cancel out.