Arithmetic Course/Polynomial

Polynomial
A polynomial is a variable that has the general form
 * $$P(x) = a_n x^n + a^n-1 x^n-1 + a_1 x + a_o$$

Here, the $$a$$ literals represent any constant numbers.

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

$$P(x) = a x $$

Consider $$y$$ as a monomial function of x.
 * $$y = 2 x $$
 * 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)


 * $$P(x) = a x + b$$

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
 * $$P(x) = a x^2 $$
 * $$y = a x^2 $$
 * x | -2 -1 0 1 2
 * y | 4 2  0 2 4


 * Parabola goes through point (0,0)


 * $$P(x) = a x^2 + c $$
 * Parabola goes through y - intercept point (0,$$\frac{c}{a}$$)


 * $$P(x) = a x^2 - c $$
 * Parabola goes through y - intercept point (0,$$\frac{c}{a}$$)


 * $$P(x) = a x^2 + b x $$
 * $$P(x) = a x^2 + b x + c $$