# Arithmetic Course/Polynomial

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## Polynomial

A polynomial is a variable that has the general form

$P(x)=a_{n}x^{n}+a^{n}-1x^{n}-1+a_{1}x+a_{o}$ Here, the $a$ literals represent any constant numbers.

## Monomial

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

$P(x)=ax$ Consider $y$ as a monomial function of x.

$y=2x$ 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)

• $P(x)=ax+b$ Equation of a straight line with slope m = 1 and passing through (0,0).

$y=x$ x | -2 -1 0 1 2
y | -2 -1 0 1 2

## Binomial

Polynomial of one variable has the general form

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