Question

what is a polynomial ? and how algebra and polynomial expressions are separated?

Answer 1

The terms in a polynomial are multiples of powers of a particular variable separated by plus or minus signs.

So if p(x) is a polynomial called p in terms of a variable x, then p(x) is defined in terms of powers of x:

p(x)=a_nxⁿ+a_n-1x^n-1+...+a₂x²+a₁x+a₀, where a_n are constants (positive or negative numbers, coefficients) and n is highest power (called the degree of the polynomial).

For example: q(x)=2x⁴-3x³-x²+5x+4 is a 4th degree polynomial in x (a₄=2, a₃=-3, a₂=-1, a₁=5, a₀=4 are the coefficients).

A binomial is, for example, 3x-2 and has a degree of 1. Algebra deals with all degrees of polynomials.