This Calculator computes the degree, leading coefficient and leading term of a given Polynomial.

## How to use this calculator?

Variable Input a single-letter that is the polynomial variable. Examples : polynomial = 4x+1 , then input variable = 'x' polynomial = 9t + 5 , then input variable ='t' Are accepted : The Polynomial variable Polynomial coefficients : must be rational numbers e.g. integer numbers (-4) or fractions (1/4) or decimals (3.6). Operators : + - * / ^ (the last is the power operator so x^2 = x^2) Parentheses : an example of use is (x^2+1)(x-5) Polynomial = x^2-4x+1 (variable = 'x') Polynomial = (x^2-1)(x-5)-3 (variable = 'x') Polynomial = x^3-4/3*x^2+1 (variable = 'x') Polynomial = 0.23*t^2-1/5*t+1/2 (variable = 't')

## What are the leading term, leading coefficient and degree of a polynomial ?

• The leading term is the polynomial term with the highest degree.
• The degree of a polynomial is the degree of its leading term.

So we can write,

\text{Leading term} = \text{Leading coefficient}^\text{Degree}

Usually, the leading term of the polynomial is written first. So, the general expression of a polynomial is,

P(x) = a_n*x^n + a_(n-1)*x^(n-1)+ ... + a_2*x^2 + a_1*x + a_0

The leading term is a_n*x^n which is the term with the highest exponent in the polynomial.

The degree of the polynomial is the degree of the leading term (a_n*x^n) which is n.

The leading coefficient is the coefficient of the leading term. So, it is equal to a_n.

## Examples

P(x) = 2x^3+x+4
Leading term = 2x^3
P(x) = -x^5+x^4+2x^3-1
Leading term = -x^5
P(x) = x^2-1
Leading term = x^2