Degree and Leading Coefficient/Term

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

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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'
Polynomial	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)
Examples	Polynomial = x^2-4x+1 (variable = 'x') Polynomial = (x^2-1)(x-5)-3 (variable = 'x') Polynomial = x^3-4/3x^2+1 (variable = 'x') Polynomial = 0.23t^2-1/5*t+1/2 (variable = 't')

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 $a_n$ .

P(x) = $2x^3+x+4$
Leading term = $2x^3$
Leading coefficient = 2
Degree = 3

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

P(x) = $x^2-1$
Leading term = $x^2$
Leading coefficient = 1
Degree = 2