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The polynomial degree is the highest variable power in a polynomial.

$p(x)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}{9x}^{3}-{3x}^{2}+8x\u20132$. In this polynomial, the highest variable power is \(3\).

$p(x)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}{3x}^{2}+8x\u20132$. In this polynomial, the highest variable power is \(2\).

**Polynomial classification based on degree:**

**Linear Polynomial**:**Quadratic Polynomial**: A polynomial of degree \(2\) — $p(x)\phantom{\rule{0.147em}{0ex}}={3x}^{2}+\phantom{\rule{0.147em}{0ex}}8x\u20132$.**Cubic Polynomial**: A polynomial of degree \(3\) — $p(x)\phantom{\rule{0.147em}{0ex}}={9x}^{3}-{3x}^{2}+\phantom{\rule{0.147em}{0ex}}8x\phantom{\rule{0.147em}{0ex}}\u2013\phantom{\rule{0.147em}{0ex}}2$.

Important!

It must be noted that there will be a maximum of \(2\) terms in a linear polynomial, \(3\) terms in quadratic polynomials and \(4\) terms in the cubic polynomial of polynomials in one variable.

General form of polynomials of different degrees:

**Linear Polynomial**:**Quadratic Polynomial**:**Cubic Polynomial**:

Important!

It's not defined the degree of zero polynomial. There can be any degree. $p(x)=0$ can be substituted as $p(x)=0\times {x}^{n}$ — where '\(n\)' can be any number.

**For example**:

**\(p(x) = 0 × x^6 = 0\).**

The constant polynomial is the form \(p(x) = c\), where \(c\) is the actual number. This means that it is constant for all possible values of \(x\), \(p(x) = c\).

**For example**: \(p(x) = 6 = 6 x^0\) [where \(x^0 = 1\)]

Note that the highest power of the '\(x\)' is zero.

Therefore, the degree of the non-zero constant polynomial is zero.