The standard form for a polynomial is defined for any real coefficients \(c_i\) and integer exponents of \(x\) with the following pattern: \[f(x) = c_nx^n+\dots+c_3x^3+c_2x^2+c_1x+c_0\]

We can also considered a factored form of the polynomial:

\[f(x)=a(x-x_1)(x-x_2)\dots(x-x_k)\]

where each \(x_i\) is a zero of the polynomial. In the case of the standard form, we say the degree of the polynomial is the value of the greatest exponent in the polynomial. For a factored polynomial, we add the exponents of all the factors to get the polynomial degree. For example:

1. \(f(x)= 4x^3-1\) is degree 3
2. \(f(x)= -\frac{{2}}{{3}}x^{{13}}-100x^2+1\) is degree 13
3. \(f(x)= -5(x-1)^2(x+3)(x+6)^3\) is degree 2+1+3=6. Note that we add 1 when the exponent is omitted.
4. \(f(x)= \dfrac{{1}}{{5}}(x-1)(x+1)\) is degree 2