UPSKILL MATH PLUS

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### Theory:

The polynomial degree is the highest variable power in a polynomial.
. In this polynomial, the highest variable power is $$3$$.

. In this polynomial, the highest variable power is $$2$$.

Polynomial classification based on degree:
• Linear Polynomial: A polynomial of degree $$1$$ — .
• Quadratic Polynomial: A polynomial of degree $$2$$ — .
• Cubic Polynomial: A polynomial of degree $$3$$ — $p\left(x\right)\phantom{\rule{0.147em}{0ex}}={9x}^{3}-{3x}^{2}+\phantom{\rule{0.147em}{0ex}}8x\phantom{\rule{0.147em}{0ex}}–\phantom{\rule{0.147em}{0ex}}2$.
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: A polynomial in one variable with degree one is called a linear polynomial. It can be denoted as $p\left(x\right)=\mathit{ax}+b$.
• Quadratic Polynomial: A polynomial in one variable with degree two is called a quadratic polynomial. It can be denoted as $p\left(x\right)=a{x}^{2}+\mathit{bx}+c$.
• Cubic Polynomial: A polynomial in one variable with degree three is called a cubic polynomial. It is denoted as $p\left(x\right)=a{x}^{3}+b{x}^{2}+\mathit{cx}+d$.
Important!
It's not defined the degree of zero polynomial. There can be any degree. $p\left(x\right)=0$ can be substituted as $p\left(x\right)=0×{x}^{n}$ — 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.