Arithmetic Course/Polynomial

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

• 
  Graph of line y = x

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,${\frac {c}{a}}$)

• $P(x)=ax^{2}+bx$
• $P(x)=ax^{2}+bx+c$