# Arithmetic Course/Polynomial

## Polynomial

A polynomial is a variable that has the general form

${\displaystyle P(x)=a_{n}x^{n}+a^{n}-1x^{n}-1+a_{1}x+a_{o}}$

Here, the ${\displaystyle a}$ literals represent any constant numbers.

## Monomial

Polynomials with highest degree as 1 are called Monomials. Monomial has the general form

${\displaystyle P(x)=ax}$

Consider ${\displaystyle y}$ as a monomial function of x.

${\displaystyle y=2x}$
x | y
-2 | -4
-1 | -1
0 | 0
1 | 1
2 | 2

General equation of a straight line with slope m = a through y intercept (0,b)

• ${\displaystyle P(x)=ax+b}$

Equation of a straight line with slope m = 1 and passing through (0,0).

${\displaystyle y=x}$
x | -2 -1 0 1 2
y | -2 -1 0 1 2

## Binomial

Polynomial of one variable has the general form

• ${\displaystyle P(x)=ax^{2}}$
${\displaystyle y=ax^{2}}$
x | -2 -1 0 1 2
y | 4 2 0 2 4
Parabola goes through point (0,0)
• ${\displaystyle P(x)=ax^{2}+c}$
Parabola goes through y - intercept point (0,${\displaystyle {\frac {c}{a}}}$)
• ${\displaystyle P(x)=ax^{2}-c}$
Parabola goes through y - intercept point (0,${\displaystyle {\frac {c}{a}}}$)
• ${\displaystyle P(x)=ax^{2}+bx}$
• ${\displaystyle P(x)=ax^{2}+bx+c}$