 UPSKILL MATH PLUS

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Consider a polynomial in one variable($$x$$).

$$p(x) =$$ $$a_{n}x^{n}$$$$a_{n-1}x^{n-1}$$$$+...$$$$a_{2}x^{2}$$$$+$$$$a_{1}x$$$$+a_{0}$$

The terms of the polynomial $p\left(x\right)$ are ${a}_{n}{x}^{n}$, ${a}_{n-1}{x}^{n-1}$, ..., ${a}_{0}$.

The coefficient of the polynomial $p\left(x\right)$ is ${a}_{n}$, ${a}_{n-1}$, …, ${a}_{2}$, ${a}_{1}$ of the variable ${x}^{n}$, ${x}^{n-1}$, ..., ${x}^{2}$, $x$ respectively.
Example:
1. Consider the polynomial $p\left(x\right)=a{x}^{2}-8x+9$.

The terms of the polynomial are $a{x}^{2}$, $-8x$, $9$.

The coefficient of $$x^{2}$$ is $$a$$.

The coefficient of $$x$$ is $$-8$$.

The coefficient of $$x^{0}$$ constant is $$9$$.

2. Consider the polynomial $p\left(x\right)={9x}^{3}-{3x}^{2}+8x-2$.

The terms of the polynomial are $$9x^{3}$$, $$-3x^{2}$$, $$8x$$ and $$2$$.

The coefficient of ${x}^{3}$ is $$9$$.

The coefficient of ${x}^{2}$ is $$-3$$.

The coefficient of $x$ is $$8$$.

And $$-2$$ is the coefficient of ${x}^{0}$.
Important!
Polynomial may have any finite number of terms.

$$p(x) =$$ ${x}^{199}$ $$+$$ ${4x}^{198}$ $$+$$ $$...$$ $$+$$$$2x$$ $$+$$ $$3$$.

A polynomial of one term is defined as a monomial. $p\left(x\right)=8x$.

The two terms are referred to as binomial. $p\left(x\right)={9x}^{3}+3$.

And the three terms are referred to as trinomial. $p\left(x\right)={7x}^{4}+{3x}^{3}+7$.
Constant polynomial: 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 $$x$$, $$p(x) = c$$. Polynomials $$p(x) = -3$$, $$q(y) = 18$$, $$r(z) = \frac{2}{5}$$ are the examples of constant polynomial.

Zero polynomial: The constant polynomial $$0$$ is called the zero polynomial. $$p(x)=0$$ is the zero polynomial.