A polynomial in one variable is expressed in standard form when the monomials that form it are arranged in decreasing degree order. This form can be represented with the following general expression.
anxn+an−1xn−1+⋯+a1x1+a0x0
In that general expression, n is a whole number and the coefficientsan,an−1,…,a2,a1,a0 are real numbers. The following expression written in standard form shows a polynomial with a degree of 5.
x5−12x4−2x3+8x2+9x+0
It should be noted that coefficients can be zero. In those cases, the corresponding terms are often omitted, which causes consecutive terms to have exponents that are not consecutive descending numbers. The following example, in standard form, shows a polynomial with a degree of 4.
3x4−2x2+6x+5⇕3x4+0⋅x3−2x2+6x+5
It can be seen that the x3-term was omitted, at first. However, if chosen to do so, the polynomial can be expressed in standard form with a coefficient of 0 and the corresponding term.